TLDR; A position that's not falsifiable requires extraordinary evidence.
The best way to bolster a claim is to test it. For example, let's say you're being sold a cleaning product that the seller claims can remove any kind of stain from carpet. Would you take them at their word for it? Probably not. Most of us will want to put that claim to the test. Demonstrate to me that this product does what you say it does, and then I'll believe you.
Falsifiability just means that the claim can be tested. A test can be devised such that I can determine whether the claim is more likely true.
Unfalsifiable claims bear a heavy burden of proof because they cannot be bolstered with testing. We recommend rejecting these sort of claims unless or until evidence can be presented to support the position.
How to Test
How you put claims to test completely depends on what kind of claim it is. You have to think first of what might make a claim false. So, if we take our cleaning product example, we could say that if there were a type of stain that it wasn't able to clean, then the claim that it can clean any type of stain is false. Now all we have to do is devise a test where we try the product on different types of stains until we find one that it doesn't work on.
When dealing with more complex topics such as politics, the endeavor can be more difficult. Our suggestion would be to not try tackling it all at once. Break down the problem into smaller pieces. If someone claims something like "Bernie Sanders would be a great president.", then you might want to narrow the scope first. Maybe start with "Bernie Sanders as president would improve the education level of Americans". This is still pretty high level stuff, but you may be able to test assumptions about this claim by verifying statistics on educational programs that Bernie espouses. If that's too big, break it down further until you have something you are able to test.