I played with bittorrents about 2 yrs ago and while I got them working I found it to be just more a pain in the ass than it was worth it. Maybe the clients have improved and there's better content available now.

Simply put you need to find any websites like isohunt or mininova or thepireatebay that carry bittorrent streams

You choose the one you want and clicking on the link should start your bittorent client and it will ownload the file

I use Utorrent as my client works great

Ah the inter-tubes... technology at it's finest.

These are places you can find stuff...
http://www.scrapetorrent.com/
http://www.torrent-finder.com/
http://www.torrenttyphoon.com/

This might be the best software out there to do it with...
http://azureus.sourceforge.net/

And last but not least a guide on how it all works...
http://www.azureuswiki.com/index.php/User_Guide

Go to bittorrent.com and download the program, when you have it installed in your computer, it'll ask you to sign onto at least one hosting website, or it'll automatically sign you onto one of several sites, then you go and sign onto whichever hosting sites you want. Basically the way it works is that you run a search for whatever you want in the bit torrent window, and the main bit torrent site will come up with a list of matches for your query. You can download whatever you want from there by clicking on 'download torrent'. However, you must be signed on as a user to the website that the torrent is being kept at, otherwise you will not be able to download the file. The website is listed on the query page under the name of the file alongside the rest of the information for that particular download.

But as a word of warning, its very hard to find specific things on there, but its great for downloading massive amounts of files, say tv series or movies or albums, but it in my experience, it can take up to several weeks to download a file, so just keep that in mind when using the program.

Everyone else has covered the basics, so I'll just add in one pointer:

One thing that, at least the last time I read through them, the documentation on both the bittorrent.com "official" client and the (much swoopier) Azereus client was very fuzzy on is the fact that you will get much, much better performance if you have at least once inbound TCP port accessible from the entire internet on the machine running your client. Port 4096 is the default, but you can use any port so long as you tell your client which one you're using.

If you have a firewall or cable modem that supports the "UPnP" (Universal Plug-n-Play) standard, Azereus can automatically configure the port-forwarding for you: look in the plugins section under "UPnP".

It'll still work without the inbound port, but you won't be able to see as many data sources, so your downloads won't be as fast.

You are ahead of me I have no idea what a bittorrent thing is let alone what it does or will do . I am old because in reading all the post I am even more confused then I was...
I am longing for the days of Check Books and Cheap Gas and Penny Candy

Show me what? a bite or a torrent?

Another vote for the azureus client.
Another vote for isohunt.com.

First you have to make an offering at the Temple of Sexual Deviance of the order of BitTorrent Brotherhood. You can guess what that ought to be like. Then you pay the government and RIAA a bribe so they won't sue you later for downloading waay too many movies. Thirdly you go to Best Buy and order a gargantuan hard drive (hmm 250 GB ought to do you for a few weeks worth anyway) and get it installed. And then you're good to go!

This sounds like the most infuriating thing imaginable. I would throw my computer across the room and just pay for stuff to save myself the ulcers. What ever happened to simple, uncomplicated piracy...such as Napster (the free version) ?!?!?!?!