The BitTorrent world is slightly unusual from a software perspective, in that the original program, BitTorrent, is quite small and light on features. I initially pulled it down and ran it, and in short order wanted something with a bit more bang to it. So I went looking.
Well, the first interesting bit I found wasn't another implementation, but was BTFaq.com. This site has lots more information for the person new to the BT-world, including/especially how to get your network setup working if you're behind a firewall. Highly recommended. And it has a few jumping-off spots for folks looking for torrents.
Ah yes, torrents. These are the little files that contain info needed to download the actual data. You download the torrent file, open that file with BitTorrent, and it'll start getting the file(s) you want. Tracker? Yeah, BitTorrent has a few new terms, but BTFaq.com explains them all very nicely, so I won't try to do that here.