Whooo... ummm... well actually the best thing for a beginner to start with might be Easytoon... it makes some great little animated gifs. Not sure where the download is these days, though... someone around here should know.
For making professional-quality television or feature animation, my studio wreaks havoc with CORE Retas!, a Japanese program which sees heavy use in Asia, but I'm not sure how widespread it is here in the States. And it's pretty expensive (couple grand).
Its pencil test software, Quickchecker, is pretty good stuff for just learning the specifics of actually drawing animation, but it's a Mac-only program.