BitTorrent is basically a protocol that doesn't rely on central servers; instead, everything happens directly between active users.
1) Just grab a BitTorrent client. I use Comet, which is pretty solid and easy to handle, though there are plenty of other options out there. You shouldn't need to mess around with port forwarding or anything like that later on.
2) You'll need to find some torrents. A torrent is just a tiny file that holds the info on where the actual files are located. There are various torrent search engines, but I usually stick to
www.torrentspy.com since they host them and have a decent selection. Once you find what you want, just click it to download the torrent file. That should automatically trigger Comet to start the download.
3) Comet actually has built-in search sites too, but a lot of them are dead now, so I mostly just use the one I mentioned above.