The only tool you need to write addons is a text editor. There is a nice list of them on the wiki under
Author resources.
The best way to get started (for me, its how I learn) is to look at some of the simple addons others have made to get an idea how things work even get your hands dirty and modify their code to really see how it works. Once you can understand how the basics work dive into the API documentation and find things that are needed for your project. If you don't find those things talk to other authors most are very helpful and might know of ways around the problem, and if its not in the API suggest it.
Start small even if its just a "Hello World" addon and continue to add things and have fun doing it!