Since Java is inherently designed to be multi-platform, it can be developed on just about any modern computer / operating system. For basic development, all you need is a development kit (JDK). The main producer of JDKs is Sun (they provide 32-bit and 64-bit versions for Windows, Linux and Solaris), and their JDKs are all freely downloadable. To run your programs you will need a JRE (the JDK includes one of these).

The tools in the JDK are mostly command-line driven, so unless you are daunted by feature-packed graphical user-interfaces, you will likely want to use a development environment (IDE). Most Java IDEs are themselves written in Java (!!), and so can run on the same set of platforms. Probably the most popular IDE at the moment is Eclipse, not least because it too is free to download.

With a JDK (and optionally IDE) installed you have all the tools you need to write complex Java programs. However you soon appreciate that there is a LOT to learn when it comes to Java, which is where we come in ;-)