Well first off, you'll need a client.
Tomato Torrent or
BitTorrent will work on the Mac, though I prefer BitTorrent.
Next you need web sites to download stuff,
www.suprnova.org is the one I like best. But there are others that I'll let other people recommend, like MTKA.
Go to the torrent site, find something you want to download, click on the link and it should begin to download, that file is called a
torrent. Then go to your bittorrent client, choose file>open, then select the file you just downloaded.
It can take a while to download stuff on BT because BT doesn't work like Kazaa or LimeWire. BT works like this: Imagine you have a 100MB file, bittorrent will break up that file into 100K bites (the size varies) you start to download that chunk, then you start to share that chunk. So basically, if you happen to download a movie** you will not necessarily start to download the beginning of the movie, you might start at the middle or end.
I'm probably missing a few points, so anyone else fell free to correct me.
** as always, I do on *officially* support the download of copyrighted material, ex: music, movies, ect. You can still be fined/jailed for sharing copyrighted material.