Take those things, write automated tests to test them. Run the automated tests instead of testing manually, every time you can. Especially when making changes don't run the software yourself to see if your changes did what you wanted, write a test to do it and run that. The first time one of your tests catches a bug that you never would have expected, you'll be hooked.
"Test-Driven Development" actually refers to (almost) always writing the tests _before_ you write the code they test. Not everyone subscribes to this, at least universally. I wouldn't worry about that for now, I think if you just start writing automated tests every time you would have been manually testing, you'll be on the path and things will fall into place.