Even if you don't write the tests up front, you can still benefit. I once gave a testing talk to a crowd of programmers who used C#. I mentioned CSunit and one of the programmers just took off and started using it on a large app that he had built. Several days later, he mentioned to me that he had found several long-standing bugs that he never knew about (in my experience, this is common for people starting testing).

I'd start with Test::Tutorial and just start writing a few small tests for something you've worked on. That should get you the feel for it. If you're programming in another language, check out testing tools for your language. (They even have them for Javascript).