Different sciences operate in somewhat different ways, due to the nature of their subject matter and the constraints on scientific method. 
In general, we get a difference between historical-explanatory sciences and mathematical-experimental ones, with a continuum of transition from one kind to the other. We see the elements of the sciences in the accompanying diagram, which begins at the top with observation.
From Aristotle to Francis Bacon and beyond, the notion has been that science begins with observation. It is now clearer, however, that the concepts that they would have thought sprung from observation in fact must often anticipate it, informing what it is that we are looking at, or for, in our observations. This circumstance is discussed elsewhere in relation to Karl Popper and to Hermeneutics. 
As concepts and observations feed off of each other, we see the Hermeneutic Cycle of interpretation, as with Popper we get a cycle of "conjectures" and "refutations."
Below the concepts, we get their mathematical formulation, or simply a historical record of observations, or the record of historical changes. The latter may give rise to mathematical formulation, or may not. The purpose of all this, of course, is explanatory, but a historical record, or even a mathematical formulation, may come up deficient in explanatory power. Most distinctive of modern science, then, is the predictive power of its theories, most dramatically demonstrated in the mathematical theories.
Modern science begins with the most perfect mathematical-experimental science, which is physics. Most of the phenomena studied by physics are things that are happening all the time, like objects falling, or that can be staged as an experiment, like Galileo dropping (or rolling) cannon balls. This characteristic continues today, when fundamental physics depends on the high energy collisions of sub-atomic particles. These can be studied as cosmic rays bombard the earth, or they can be created in particle accelerators. The great innovation in physics introduced by Galileo was the application of mathematics to motion. This feature came to all but dominate physics with Issac Newton. Even today, many people think that a science is not properly scientific, or scientific at all, without a mathematical element. Given a theory, there is also a large predictive element in physics, so that observations and experiments are not just matters of seeing what happens, but of seeing if what we predict is what happens.
On the other hand, while the concepts of physics might be expected to enable different theories to explain why events happens the way they do, this does not always happen. In recent physics, Quantum Mechanics is a theory that creates real puzzles about why nature works the way it does. Some physicists, like Richard Feynman, rather enjoyed the strangeness of it and simply gave up on trying to squeeze out any real explanation. Nevertheless, this is not a satisfying situation. One attempt to avoid that is through Positivism, in which the meaning or explanation doesn't matter, only the predictive power of a theory. Another attempt is through the notion that the meaning actually is in the mathematics, which is self-explanatory, and not in the concepts otherwise supplied by the theory -- this is what happens in the "Sin of Galileo." Both of these are simply reductionistic attempts to avoid the challenges of explanation, or of a conceptually satisfying theory.
If it was impossible for science to explain why its predictions come true, this would be a grave disappointment to any historic scientist, and a repudiation of the very word "science," i.e. scientia, "knowledge." The mathematician Roger Penrose finds it difficult to understand how a scientist could entertain such a view. At the same time, mathematics alone is not enough to provide the meaning of scientific theories, since the equations of science use unit terms like "mass," "distance," "time," etc. that stand for physical realities whose use can be stipulated for scientific work but whose explanation may even lead into metaphysical issues.
At the other end of the spectrum from physics we get historical sciences like geology. 
Here much of the observational data is evidence about the past and about processes that may not happen very often, may not be happening now at all, or that happen slowly over such long spans of time that even all of human history (5000 years since the I Dynasty of Egypt) is not enough to see much of an effect. The geologist looking at rock strata, or the paleonologist digging up bones, or a zoologist describing a new species, does something that a physicist may dismiss as "stamp collecting." But no physicist ever would have known that there had been dinosaurs.
In dealing with history, the relevance of prediction and of mathematics may fade away, and scientific issues may even become confused with philosophical or metaphysical issues. Nevertheless, prediction is not unheard of. When James Hutton speculated (1785) that the earth had undergone countless cycles of erosion, deposition, folding, and uplift, and he imagined the consequences, he was able to make a prediction that he subsequently confirmed himself. 
That is, he predicted the existence of unconformities in strata of rock. Thus, old strata may have been uplifted from the horizontal and eroded down across the grain, upon which younger depositions have been laid down, horizontally and undisturbed, lying "unconformably" upon the older strata. This is what Hutton found, on exposed cliffs, by 1787. Sometimes the record of a great deal of time is lost, whole geological Eras, within an unconformity. 
A record of erosion, folding, uplift, and deposition can become complex indeed.
A good example of a concept in geology that was without much explanatory content, let alone a predictive or mathematical one, is that of the "geosyncline." Discovering great wedges of strata in the earth's crust, shallow at one end and deep, often many miles deep, at the other, geologists formulated the idea that the strata accumulated as a area of the earth's crust was depressed. They didn't know why the crust was depressed, and sometimes the thinking was that the weight of the depositions itself weighed down the surface and depressed it. This was a "geosyncline," often mirrored by an "anticline," a corresponding area that rose and from which strata were eroded. These distinctions explained so little that it may be just to call them "descriptive" rather than either "explanatory" or "predictive" concepts. The geosynclines in time seem to rise into mountain ranges, fracture, fold, and erode. Some of the thinking about this was that maybe the weight of the strata fractured the crust of the earth, causes the mountain building ("orogeny"). None of this, however, was much of an explanation, with little return to the size of the speculative element introduced.
Eventually, the dynamic of geosynclines and anticlines was revealed through the theory of Plate Techtonics. Continential Drift was a theory that had been around for decades (beginning with Alfred Wegener, 1912, and others), based on continuities in life and rock formations between continents now separated by oceans, and on the shapes of continents themselves, like Africa and South America, that look to have fitted together quite nicely. However, few respectable geologists regarded Continental Drift with more than derision. Why? Because, in the absence of an explanation for the drifting, the whole idea seemed preposterous. As noted, however, the absence of a similar explanation for the formation of a geosyncline was hardly regarded as an embarrassment. The evidence of the sea floors, with new rock emerging at mid-oceanic ridges, and the age of the rock rising steadily outward from the spreading centers, then set off a revolution in geology. With a sequence of concepts (Continental Drift), observation (sea floors), and new concepts (spreading centers, subduction), whole new perspectives and revelations on geological history suddenly emerged. The reality of this did not burst upon the public until the 1970's.
Even geology can have its mathematical element, though often this involves matters borrowed from physics (like radioactive dating) and chemistry (minerology and petrology). Where the predictive and mathematical element fades away, however, the issues can become muddled. This is what we see with one of the defining principles of biology and paleontology: the Theory of Evolution by natural selection. The theory addresses vast amounts of observational evidence -- the variety and antiquity of life, the close similarities of many forms of life within that variety, and the manifest succession in time of those similar forms of life. In terms of simplicity of explanation (Ockham's Razor), it is natural enough to expect that the successive forms of life have arisen from each other. The desire to deny this principally derives from a religious disinclination to credit natural explanations.
Thus, the current vogue of "Intelligent Design" in the anti-Evolution ranks relies on arguments derived from metaphysics and natural theology. That an Argument from Design (for God) had already been subject to a critique in philosophy, by Hume and Kant, seems to be overlooked by people who would actually rather rely on Aristotle or St. Thomas. They thus betray, not just their ignorance of science, but of the history of philosophy. For, indeed, "Intelligent Design" is not a scientific theory at all, but an argument against the possibility of any scientific, i.e. empirical and naturalistic, theories about the history of the earth or the origin and development of life. It apparently doesn't bother them either that the theology implied by their efforts, that God is constantly dropping new and different, but improved, species down onto the earth, to replace ones that have died off (or perhaps been killed off by divine intervention), would offend most historic theologians with the carelessness, lack of foresight, planning, and, indeed, intelligent design of God -- it would be enjoyable to see them in debate, for instance, with Leibniz. Their efforts, however, are so confused that they probably don't even get as far as that point.
The source of that confusion, however, is of great significance. Many of the defenders of science (e.g. Richard Dawkins) against the anti-Evolutionists simply reject religion altogether, either unaware of the metaphysical issues that arise in science or comfortable to adopt the anti-metaphysical doctrine of philosophical schools like Positivism, Wittgenstein, or a "post-modern" non-cognitivism, nihilism, etc. (where these approaches actually tend to drift into attacks on science itself). The case for science can be thoroughly muddled by philosophical issues, and if the core religious beliefs of many people are openly attacked by some who believe that science and atheism are logically necessary for each other, it is not surprising that the response is attacks on science as such.
Although "Creationism" even attacked general geology, physics, and chemistry, the (academically engaged) anti-Evolutionists mostly seem to have given up that approach as hopeless, narrowing their focus just onto Evolution itself. Without a strongly mathematical and predictive theory, indeed, Evolution is vulnerable in terms of the paradigmatic elements of modern science, defined and inaugurated by the practice of physics. When the argument becomes much more conceptual and explanatory, the boundaries between science and philosophy, or even science and ethics, become, if not more difficult to draw, certainly easier to obscure, and more evidently subject to just how science is to be defined -- a matter of dispute within science and philosophy of science themselves. Nor does it help when scientists or philosophers reject the conceptual or explanatory side of science as unnecessary or meaningless, when this only has a hope of applying to physics, and not to any other science, certainly not the historical-explanatory ones.
It is thus essential to keep in mind the variety of the sciences and the different issues that arise in relation to their subject matter, methods, and tools. If physicists or mathematicians disdain concepts, explanation, or history, they actually prepare the way for the attacks on historical sciences by those with agendas that are only alien and hostile to the purposes of science. At the same time, Positivist and non-cognitive interpretations even of physics prepare the way for "post-modern" critiques of the objectivity of science, attempting to subordinate science to "politically correct" ideological purposes. There is little of the scientific spirit left either in the religious appropriation of biology or in leftist political interpretations of all of science.
An interesting case in the classification of the sciences comes with those historical sciences concerned with the study of human beings. Before any of them existed, there was history itself, now generally regarded as one of the humanities more than one of the sciences. History is defined and limited by a particular datum, the written word. Its paradigmatic form, however, the written historical text, a narrative or chronicle, was a comparatively late development in what we would now think of as historical time. Also, written texts tend to be preserved long after the period in which they were written, which means that they can become corrupted in anachronistic ways. How historically accurate are the "historical" books of the Bible, or for that matter the Iliad, is a typical problem. Checking these against contemporaneous evidence is done best by using epigraphic texts, i.e. inscriptions made at the time of the events and left on monuments, temples, tombs, palaces, ostraca, etc. In the absence of books written by historians, epigraphic evidence may be all that there is to "history."
Thus, no narrative histories or chronicles existed for the history of Egypt until Manethô, who himself was writing in Greek under the influence of Greek historiography. All the rest of the history of Egypt, and the only contemporary evidence from dynastic Egypt, is epigraphic (there are surviving papyri, including the Turin king list, but otherwise none are written as expositions of history). This is often infuriatingly fragmentary and obscure. The epigraphic evidence, however, exists in the context of a science, 
namely archaeology [from arkhaios, "old" -- arkhê, "beginning" -- and logos, "talk," "discourse"], whose study is the physical remains of cultures and civilizations, often still living ones, but characteristically ancient and vanished ones.
In archaeology we have the challenge of forming a picture of human life, if not history, from the physical remains of the culture. In the absence of people to ask, the artifacts must speak for themselves. They can do that better if inscribed, but then archaeology as such deals with objects whether they are inscribed or not, or whether the inscriptions can even be read. The archaeologist looks at humble remains, like pots and baskets, or monumental ones, like temples and tombs. Either way, the issues are often the same: sequence, dating, function, influence, materials, technology, etc. Enthusiasts hoping for the life of Indiana Jones, however, should be aware that the basic techniques of the science are more concerned with the careful excavation and preservation of the humble objects, while running off with some precious artifact snatched from its milieu is generally called "looting" and is usually a crime both in local law and international convention.
Rich archaeological sites often involve burials. This leads to the next science, physical anthropology [from anthrôpos, "man"], by which human remains are studied. Physical anthropology, however, extends fully into the present, where the physical varieties of the human species are studied, and deep into the past, where we see the predecessors of modern humans, and the pre-human hominids of even earlier time. The archaeology thins out steadily as we go back in time, and soon we are in the context of sciences, like paleontology [palaios, "old"], where the remains of the ancient animals associated with humans and hominids would be studied, and geology [gê, "earth"], where the ancient world itself is reconstructed. Modern physical anthropology can involve "purer" sciences, like anatomy and physiology, and it also has practical applications, like "forensic" anthropology, where the pathologist and the medical examiner must call in the bone expert, the anthropologist, for conclusions about skeletalized remains. Dr. Bill Bass, with his famous "Body Farm" Anthropological Research Facility at the University of Tennessee in Knoxville, was a physical anthropologist who became one of the pioneers of forensic anthropology.
The physical anthropologist working on modern, living people is liable to rub shoulders
with the cultural anthropologist, who studies the social and physical culture of living people. Now the artifacts do not need to speak for themselves, since the anthropologist can ask about them and see how they are used. Often this can illuminate the archaeology of people who are no longer around to be asked. We tend to associate cultural anthropology with pre-literate people living in remote locations, like tribesmen in New Guinea, but the discipline is not limited to such people, and people living in literate, modern, and technological civilizations can as easily be the subjects of anthropological study. As such, we get a bit of overlap with more general social sciences, like sociology. Unfortunately, in both cultural anthropology and sociology also, there is a history of the disciplines being infected with ideological or political agendas -- e.g. relativism or Marxism. Other disciplines are not free of this, but one can get the impression that cultural anthropology and sociology are often dominated by the agendas, producing tendentious studies which are discredited by their own bias. This is unfortunate, and the popularity in the humanities and social sciences of "deconstruction" and various forms of English Department Marxism, often called "Theory," is no help at all -- these ideas exist to justify ideological bias, and they are fundamentally opposed to real science and even logic. This is part of the danger already noted for historical sciences in general. By contrast, digging carefully in the dirt to find archaeological artifacts or bones seems more like the stark honesty of pure, empirical science -- living in conditions that would probably be shunned by most academics.