Think of bittorrent as a multi step process.
1. You need a client program to work with the torrent system. I use Azureus myself.
2. Then you visit a torrent search website (typically, like the torrentreactor.net site mentioned above) to looks for torrents of content you'd like to download.
3. From those sites, you get linked to a .torrent file, which is just instructions for your bittorrent client program to find and download the correct content. Download and save that file to your computer.
4. Once you enter that torrent file into your client program, it connects to the "tracker" for that torrent which keeps track of who is currently active with that torrent, be it "seeding" (has a complete copy of the content for upload) or "leeching" (currently downloading content).
5. Once the torrent starts running it will connect to and start downloading small pieces of the content, usually from a combination of the available seeders and leechers. Leechers upload individual parts as well to other leechers. The client program assembles the individual small parts into complete files.
You are completely at the mercy of their upload bandwidth (in combination) as to how fast you can download. There is no central location of the content, if no one currently online is "seeding" then you can't download a complete copy, all you can do is leave it running and hope someone comes online that has it available. I've left torrents up for days or weeks waiting for them to download, that's the nature of the system sometimes. Popular content will have lots of users so better speed and the longer the torrent will stay active.
ETA:
I found quickly that the best way to use bittorrent was to have a separate computer for it, that I could leave running for long lengths of time uninterrupted.
Also recommend that you have a very good firewall on your computer, and make sure it's updated.