First off, you'll need a Java Development Kit (JDK), freely available from Oracle:
You will also probably want an Integrated Development Environment. I'm at least passingly familiar with three, so those are the ones I'm linking here. They're in alphabetical order, don't take the order as being an endorsement of quality, all three products will let you build stuff easily enough:
You may want to download Git as well. While this is certainly not required to get started, using it will make it easier to grab updates as I made them. Git is integrated pretty well into IntelliJ, I can't speak to how it works with Eclipse and NetBeans:
I'll continue to update this page with other software I mention. Come to think of it, I haven't mentioned GIT yet. I should probably put up a post about pulling the source code examples for the blog...