We Don't
Political scientists do not validate empirical claims. It might seem counter-intuitive if your background is not in the sciences, but we generally focus on disproving statements rather than proving them.
Why? Because in practical terms it's nearly impossible to prove anything. Non-experimental sciences work through induction: we collect observations and then posit an explanation to generalize those observations. However, we can never be certain that this generalization is correct, because it's always possible there are conflicting observations that we didn't see (this is the problem of induction).
Go ahead and posit a hypothesis. A classical example is "all swans are white". To prove (or validate) that hypothesis we would need to observe all swans that exist in the past, present, and future. That's impossible and not really a fruitful way to conduct research. Instead, we would focus on disproving the statement by restating the hypothesis as "There exists at least one non-white swan." This could be proven by observing a non-white swan, although the only real value is that we proved that not all swans are white. This is to say that we falsified (or disproved) the original hypothesis.
If you want to know more about the general philosophy of science utilized in political science, you'd want to focus on the works of Karl Popper. He was really interested in what separates science from non-science and how we should approach proving or disproving things.
Research Methods
How do we actually falsify things? I'll cast this broadly, but the general idea is that we hypothesize the existence of some fact and then try to collect the dis-confirming evidence.
We have two fundamental approaches, both stemming from the philosophy of John Stuart Mills:
- The Method of Similarity: Take a collection of things you expect to be the same and look for differences. For example, a famous hypothesis is that cultures that emphasize trust have more efficient governments (Further reading: Making Democracy Work). What we could do is take a bunch of regions with low trust and observe their efficiency. If we observe that some of those low-trust regions actually have very efficient governments, we would have disproved the hypothesis.
- The Method of Differences: Take a collection of things you expect to be different and look for similarity. Using the same hypothesis, we could include some low-trust and high-trust regions in our study. If we find that both kinds of regions can have efficient governments, we have disproved the hypothesis.
If we can't collect any dis-confirming evidence, than the formal logical statement is that we have "failed to disprove the hypothesis". Since we can't prove anything for sure, failing to disprove it is the best we can do.
Hopefully later someone will come along and disprove our hypothesis - that's how science progresses!