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It is asserted here (time stamp 10:04) that

My opponent [referring to Maxine Waters] only passed 3 bills in Congress in 27 years.

Is this true and how does an average person like me verify this assertion (and others like it)?

In my own effort to answer this, I looked into votesmart.org and govtrack.us. At a very cursory glance, the assertion seems false as Waters voted on more than 3 bills that at least passed the House. But I'm not confident in my judgment as this is the first time I think about checking this kind of assertion.

I have no stake in the assertion being true or otherwise. In the interest of giving the assertion some benefit of doubt, however, is there an interpretation of the assertion that makes it true?

From the Advanced Search for Legislation page, it appears that Representative Waters has sponsored 5 bills since 1973 that have been enacted. Three of them were enacted and signed into law and the other two were incorporated into other legislation and subsequently passed. I would assume, to be charitable, that the two bills that "didn't count" were overlooked by mistake.

On that same page, you can see that she sponsored, or is currently sponsoring 338 bills from that same time period.

The information you're looking for is available on govtrack.us, but you need to know what to search for.

In this context, "passing" a bill (without any qualifiers) generally means introducing it and having it become law. It may or may not include bills which were merely co-sponsored, but in my experience, when they do, it's explicitly called out.

Given that, the following search will show you that she has, in fact, only introduced three bills which were passed:

If you want to include Concurrent Resolutions, which are bills that both houses agree to but aren't actually laws, then she's passed five bills. Simple Resolutions (bills that pass a chamber but don't even go to the other one) add three more, for a total of eight. However, it's reasonable to not include resolutions, since they have no binding impact and are often passed without a formal vote.