Science starts out with one core assumption: that a shared reality exists, and that our senses can provide a more or less direct - if imperfect - representation of it.
Then it's just a matter of observation which methods tend to get the most accurate results. Objectifiability, observation, prediction, repeatability, consistency, and so on. Science has a bunch of methods in addition to logic and mathematics. They have already been linked so I won't repost them.
One of the more difficult aspects of advanced models in physics (basically any post-Newtonian theory) is that they strive to describe things that we have no notion of. We describe electrons as if they were particles (in terms of matter) or as if they were waves (in terms of patterns). Whether they are either or both is sort of a metaphysical question. It becomes less of a question of what's actually true and more of a question of how accurately we can describe it.
But there is the nigh-certainty - remember, nothing is considered proven in science - that atoms exist. It's not an assumption, it's a conclusion drawn from available data. The theories describing atoms are demonstrably imperfect but at the same demonstrably more accurate than anything else we have. And we're not talking "about ten times better then a guesstimate".
Now, with the existence and some things about the nature of atoms already established, the theories progressed further. It's still technically possible that at some point the whole thing took a wrong turn and that a new theory emerges that ditches the entire concept of atoms and is still as accurate or more so. Considering we have been using the constantly refined atomic theory to build atomic and chemical reactors as well as creating all kinds of new compunds for our technologies, I find it hard to believe that we could have stumbled upon a model that is so very workable and yet at the same time so dead wrong.
Let's make it a bit more accessible though and take plate tectonics as an example. In simplified terms, we know that the shores of the continent match those of distant continents surprisingly well. We also find, in certain strata, that fossils are distributed in, say, the West coast strata of Africa and the East coast strata of South America, as if there weren't an ocean in between.
Now we might conclude that the continents were once connected. So we have a hypothesis. Now let's see ... we have an observed phenomenon explained, check. Our hypothesis is falsifiable (if we go out and look for evidence, it's possible we'll be proven wrong), check.
So we still need predictions and, if at all possible, a mechanism, i.e. a reason why the continents move.
Predictions are relatively easy in this case. If we're right, we should find matching fossils we have not yet seen in certain strata of continents that appear to fit together - but also be able to localize strata where the fossils no longer match because the continents drifted away from each other. It doesn't matter that this is basically what drove us to the conclusion in the first place, as long as we don't content ourselves with just the fossils we already know. While we're at it, we also compare geological formations, if the kinds of rocks match up and so forth, localize geologically active zones etc.
Another prediction would be that the continents are still moving. All kinds of stuff follows from that. For example, that rock that was once sea floor could now be a massive mountain; thus we can go look for fossils high above the shoreline. If we're lucky and technology has progressed far enough, we can even measure how fast the plates are moving today.
And if we're really lucky, physics will have provided the means to explain the basic functioning of the Earth's core, providing a mechanism (nuclear decay), maybe even a time frame.
This is simplified of course, but these are the kinds of things we'd have to do. You start with a deduction, think about what would need to be true for the deduction to be accurate, what follows from the deductions, and always, always check against reality. Thus you have an idea that binds some facts together - the idea can be arrived at any which way - which is tested a bit and becomes an ad-hoc hypothesis. Further testing will show whether it deserves to be called a hypothesis and if it's fleshed out thoroughly and isn't disproven for a while it'll be called a theory. Sometimes theories are so well-founded they are generally taken as fact (such as the heliocentric model) but if scientific conduct works as it should, their details are still refined - and more importantly, if someone comes up with a model that's even better, the old one will be ditched.
Contrast this with faith, where no checking against reality is required. Faith can be consistent i.e. non-self-contradictory, but it isn't falsifiable - and where it is, it typically contradicts scientific findings which, if not entirely true, are at least demonstrably accurate. In both thought systems, ideas can be arrived at completely arbitrarily, yet only bothers to check them against reality with any kind of rigor.
If it's faith I have in science, it's a different kind of faith than faith in a being that adds no descriptive power to our understanding of the world. An explanation with personal significance that provides sense to someone is not the same as a scientific explanation - just as my opinion that the atmosphere is made of nitrogen, oxygen, etc is not the same as my opinion that the haftargian Shmoople colored it blue. Both are opinions but they are arrived at by wildly differing systems of thought.
Even assuming that my faith in general relativity is the "same" as a belief in god(s) ... why wouldn't I go with the one that makes GPS possible rather than the one(s) that claims to have it all figured out yet can do no such thing? Why wouldn't I go with the models that can tell me exactly why and what they do better than their scientific competitors rather than the one that can't even say why it should be taken more seriously than any other religion?
Faith isn't about accuracy. It's about feeling good and arriving at personally satisfying answers. Science is all about accuracy. It cares only about what's true for everyone, regardless of what you might think of it. At least if you accept the workability of logic.
I hope that helps.