Taking your question specifically as "how does the philosophical tradition reconcile faith and science"?
- Socrates: Socrates studied science in his youth --he found that it was great at answering questions of "how," but not great at answering questions of "why." This is still true. Science has made great strides in the last several thousand years in explaining the mechanics of the world, but the big questions about "why?" remain as unsolved as ever.
- Plato: Plato's key claim is that it's more difficult to explain the good in the world than the evil. The evil in the world is just things not working. The good in the world demands some deeper source than just the superficial mechanics of the world grinding around.
- Descartes: Descartes' insight was that we can form or receive plausible, consistent, sensible explanations for what we perceive in the world (i.e. science), but we cannot prove those actually represent a valid external reality. We essentially have to accept on faith the proposition that the world is largely as it appears to be. (This argument is actually strongerstronger now than it was when it was first crafted because of the increasing plausibility of virtual reality.)
- Pascal: Beyond the specifics of Pascal's wager, Pascal basically determined that there are a wealth of potential advantages and no real downside to being open to the reality of faith, even as a person of science.
- Kierkegaard: Kierkegaard's observation is that the world is essentially absurd and paradoxical, particularly as experienced from a human perspective. The orderly scientific perspective has its advantages, but it is not particularly representative of the majority of the human experience.
- CS Lewis: Among the theological ideas Lewis explores in his Narnia series, one is that having a naturalistic explanation for a given phenomenon does not also preclude having a divine explanation for the same thing. In a mystery book, is the gun left in the parlor because the murderer dropped it, or because the writer put it there? Both answers are true according to different perspectives.
In summary, the tension you experience between faith and science is not unique to modern times. As such, it has been addressed extensively in the philosophical tradition. You may not find any of these above viewpoints compelling, but hopefully you can see how people can be familiar with a scientific viewpoint and still find faith a necessity.
(I apologize for giving such a sketchy gloss on each philosopher's position, but your question was too broad to go into any great detail on any given response.)