I've never done it myself because it is most likely illegal, ahem, but from what I've heard, it's pretty easy to do.
For a very simple explanation, when someone uploads a torrent, they are creating and sharing a file that links back to a location on their computer with the shared data. Once other people have downloaded it, they also share that data with other people accessing the file. The more people who download/share, the faster the download speed. If you were to connect after 10 people downloaded the torrent, you would be getting parts of the whole share (bits) from different sources. There are better, more technical explanations for how it works online if you are interested.
The best software for OS X, from what these shady people tell me, is Transmission. Download your Torrent client of choice, then google for what you want to download. Include 'torrent' in your search. It won't be hard to find. If you're lucky enough to know someone who is a member of a specific torrent site, ask for an invite. There are loads of great sites that cater to all different interests. There's one whole site dedicated to Smiths bootlegs and another just for Joy Division/New Order bootlegs. Sites for UK TV shows and some general interest/random sites too. It won't be hard to find.
Download a torrent file and then simply drag & drop on the application or doubleclick. On a Mac you may need to get info on the file and select Transmission to open all torrent files. It may be necessary to designate a specific location where you want the files to live on your computer. For example, you could create a folder inside your Music/Media folder called Torrents and set that in the preferences of the application as the default location.
Good luck and use your new powers for good, not evil!