This article is not exhaustive; it covers only those topics that are seen as central by all of the major philosophies of science. As with the philosophy of mathematics, there tend to be 'schools' of scientific thought, each of which adheres to its own principles. 'Each of these in future deserves its own article(s)'.
One of the most central principles in the philosophy of science is that of empiricism, or dependence on evidence. Some claim that empiricism is necessary for science -- perhaps most notably the British empirical school. Essentially, we gather information in ways that ultimately lead back to our senses, via empirical methods that many humans are capable of experiencing. Once reproduced widely enough by many scientists, this information becomes evidence, upon which we base our explanations of how things work.
Given enough reliable evidence, one can then use the principles of reason and logic (and other quasi-empirical methods which complement the strictly empirical structure of experiment but which lead back to our sense of truth and invoke key conceptual metaphors) to work these explanations into a coherent, self-consistent structure. The degree to which one can trust such methods is a major concern of the philosophy of science. Modern definitions of reason and logic certainly have not been applied through the entire history of the scientific method, but results achieved by those earlier methods are still valid, and are very rarely invalidated. This suggests that our unchanged conceptual metaphors (such as the ideas of similarity and sufficiency that drive counting and measuring) may be more deeply rooted than any of our explanations of our thinking processes as humans, and as scientists.
Another central, but increasingly challenged, premise in the philosophy of science is the principle of falsifiability, first formally discussed by Karl Popper. This principle states that in order to be useful (or even scientific at all), a scientific statement ('fact', theory, 'law', principle, etc) must be falsifiable, i.e. able to be proven wrong. Without this property, it would be difficult (if not impossible) to test a scientific statement against the evidence.
Critics of this principle tend to follow one of two lines of argument. Firstly, they argue that theories are often accepted and built upon as a result of their eloquence and elegance, e.g. mathematical simplicity, and that experimental evidence rarely 'falsifies' but rather limits the application of such theories. These arguments tend to focus on the weaknesses of the logical law of the excluded middle, i.e. 'no gray areas', on which the principle of falsifiability depends.
The second criticism is that many scientific theories are simply not so falsifiable, e.g. those in the social sciences which are still called 'sciences', and very abstract models, e.g. string theory, Standard model in particle physics which can only be empirically tested by very expensive tests and specialized apparatus, and so are amenable to a great deal of cultural pressure and groupthink all pushing the scientists to agree, and not to test the central tenets of a theory, if such tests are feasible at all. These arguments tend to focus on the trust of the general public in the scientific community and its works, and the degree to which falsifiability actually drives what is called 'science' in the academies, research labs, textbooks, and governments.
Occam's Razor is another notable touchstone in the philosophy of science. William of Occam (or Ockhegm or several other spellings) suggested that the simplest account which 'explains' the phenomenon is to be preferred. He did not suggest that it would be true, or even more likely to be true, though 'simpler' has very often turned out to be more likely to be right (in hindsight) than 'more complex'.
Occam's Razor has usually been used just as a rule of thumb for choosing between equally 'explanatory' hypotheses (ie, theories) about one or more observed phenomena. However, it is rare that two theories explain equally, so its use has been limited. There are now mathematical approaches based on information theory that balance explanatory power with simplicity. One such is Minimum Message Length[?] inference.
Occam's Razor is often abused and cited where it is inapplicable. It does not say that the simplest account is to be preferred regardless of its capacity to explain outliers, exceptions, or other phenomena in question. The principle of falsifiability requires that any exception that can be reliably reproduced should invalidate the simplest theory, and that the next-simplest account which can actually incorporate the exception as part of the theory should then be preferred to the first.
The idea of reductionism continues to recur in the philosophy of science - essentially, it refers to the limits of the process of breaking up phenomena or processes into smaller and smaller parts and assuming that the whole can be understood in this way.
A high degree of such reduction is essential to science itself, else it would be impossible to determine significant versus not significant measurements, differences between apparatus and of experiments, etc.. What is more, it would be impossible to rely on mathematics if one refused to reduce phenomena to numbers.
Most objections to reductionism are in fact references to what Daniel Dennett calls greedy reductionism, which he claims is just 'bad science', seeking to find explanations which are appealing or eloquent, rather than those that are of use in predicting natural phenomena. It is hard to separate the issues involved with objections to falsifiability or misuse of Occam's Razor, from those which arise due to over-reduction of a complex set of phenomena. All such errors of method or choice of theories could be said to actually be errors of greedy reduction.
A final and critical theme in science is to what degree the current body of scientific theory accepted in a given culture can be taken as an indicator of what is 'true', that is, undisputed if not indisputable. The acceptance of current theory as if it were 'true' (in the sense of theology or ideology) is called scientism, and most scientists agree it is a bad idea.
Nonetheless, public perception of science is as a source of truth and predictive power, and this is a reasonable assumption in any secular and technological society. Science tends to serve as the process of consensus decision making by which people of varying moral and ethical views come to agree on 'what is real'.
Therefore, it becomes difficult in such a society, without any stronger conception of reality based on other shared ethical or moral or religious grounds, to admit any 'reality' other than the scientific method and mathematics, which have proven themselves as the most reliable way to see past human cultures.