Run tests. Write tests. It's that simple.
Seriously. Programmers like tests about as much as documentation, but they can be fun and just as challenging. Think of it like a game -- how much can you test? Can you test something thought "untestable"? Can you get 100% coverage of all the paths?
Start by looking at Test::Simple. It comes with a document called Test::Tutorial. The basics are really very simple. Either something is okay or it isn't.
From there, pick a module you like. Start with something small, just one function. Write a few tests that prove it works.
If you're exceptionally lucky, you may discover a bug. Write a test that proves it's a bug, then write a patch to fix it. All of a sudden, you're not just a hero for testing, but you're a superhero.
If you're capable of using modules, you're capable of writing tests. It's that easy. It's that valuable. Hop to it.
Update: fixed link per converter's suggestion.