OK, lemme see if I could break it down.
Say you want to download "Shrek 2" You go to a bitorrent webpage and search for it. I usually go to Suprnova.org, they seem to have the most shit there.
So you see "Shrek 2" on the list. You click the Shrek 2 link and you are prompted to download what is called a "torrent file" The torrent file is not the Shrek 2 file, it is a small file that allows you to connect to the Shrek 2 file. Now in order to connect though, you need a bitorrent client program. You can get a number of these clients here:
http://dessent.net/btfaq/#where
I personally suggest choosing the client called "ABC" Ive had the best connects with this one. So once you have your Shrek 2 torrent file and your bitorrent client, you are ready to download. Basically you open up the torrent file and wait, its that easy.
The way it works: When you connect to download Shrek 2, you are not downloading from one single source. You are downloading bits and pieces of data from everybody else who is downloading Shrek 2 at the same time. In the world of torrents you are either a seeder or a downloader (leech). A seeder is one who has the complete Shrek 2 file on his hard drive and leaves his torrent client open with the file available for downloading. A downloader is one who is basically downloading the file. It is suggested that once you finish downloading the complete file you should leave your torrent client open so the downloaders have one more source of Shrek 2 that they could be downloading from. You get it? Everybody is sharing bits and pieces of the file to complete one big file. The fastest download times come from those torrents who have the most seeders and the most downloaders, for there is a bigger pool of data to collect from.
Does this make sense?