Start small.
Unit testing (and automated testing in general) isn't a silver bullet, doesn't always apply to every situation and can be a bit of a culture shock. That said, if you're writing software that you're selling or that your company relies on, I highly recommend adopting it. You'd be surprised how many professional development shops don't.
First, get comfortable the mechanics of creating and running unit tests with your development tools.
Then, start with a new (preferably small, but not necessarily trivial) class or method that you want to test. Writing tests for existing code has its own challenges, which is why you should start with either something brand new or something that you are going to rewrite.
You should notice that making this class or method testable (and therefore reusable) has an impact on how you write the code. You should also find that thinking about how to test the code up front forces you to think about and refine the design now instead of some time down the road "when there's more time". Things as simple as "What should be returned if a bad parameter is passed in?". You should also feel a certain amount of confidence that the code behaves exactly the way you expect it to.
If you see a benefit from this exercise, then build on it and start applying it to other parts of your code. Over time, you'll have confidence in more and more of your software as it becomes more provably correct.
The hands on approach helped get my head around the subject better than a lot of the reading material and helped fill in the gaps of things I just didn't understand. Especially where TDD was concerned. It was counter-intuitive until I actually tried it.