From LXF Wiki
How Does it Work?
BitTorrent relies on at least one site hosting the file - this site is known as the tracker. As well as the tracker holding the file, it also maintains a list of clients currently downloading this file.
The tracker URL is encoded into the .torrent file, so the BitTorrent client goes to that site and starts downloading the file from the other people currently downloading it.
When you're downloading the file you're known as a 'peer'.
Once you have the have the whole file you become a 'seed'.
A torrent with no seeds is known as 'dead'.
General Bittorrent etiquette says that you should upload at least as much as you download, as this helps spread the more 'rare' parts of the file around and make it easier for other people get the file.
Where can I get it?
If you want the 'bleeding edge' then you can download a tarball from the BitTorrent website. If you're running a rpm/deb based system then your distro probably came with a version. If you're running Gentoo then just emerge it.
There are also LOADS!! of other clients available to use - just do a google search.
How do I use it?
To use BitTorrent to its maximum potential you need to open ports: 6881..6889. This allows other people to upload your file faster.
If you're using the official client when you click on a .torrent file in your web browser, it'll probably ask you what you want to do. When it does this, use the 'Open with' dialog to browse to where BitTorrent is installed and choose the btdownloadgui.py file.
Otherwise just choose the client application.
This should open a new BitTorent dialog which will probably ask you where to save the file. It's probably a good idea to save the torrent too - saves time trying to find it next time.
BitTorrent downloads can be stopped at any time and restarted by pointing the save directory to where the partial file already is.