All .torrent files are is a list of information on the files that are to be downloaded and their location on the internet through a "tracker" server. When you open the file, you'd open it with a Torrent Client (such as uTorrent). The Torrent client would then open the file, read its data, and connect to the Tracker Server which is listed in the torrent.
Some Tracker Servers are Private Trackers, meaning that they are available only to their clients. Most of these are free to sign up, however some require an invitation from current users to sign up. This is done to ensure that users properly seed their fair share of the bandwidth they download.
Seeding is the process of uploading the file to the server during and after you've downloaded the file(s). It's a good idea to seed the torrent after you've downloaded it as Torrents are seeded by the users who download the files. A good ratio to seed to is 1.5:1 (all of what you downloaded, and half as much more) or more.
Most people think that Torrent files are for illegal copies of software, games, and music; this is vastly untrue. Where the "black"/"grey" areas of Torrent files do cover illegal downloading of licensed goods, there are many legal torrented files as well. For example, a lot of "Open Source" software (such as Linux, Unix, Open Office, etc) can be downloaded through the bittorrent protocol.
Configuring a torrent client is quite easy, simply download a client (such as uTorrent), install it, set your download directory, and start your downloading. Some users, namely those behind a router, will need to forward a port on their router to their computer; this will ensure that you can properly be connected to so that you can seed your torrents. This port will vary from client to client, and most will allow you to set the port within its configuration.
Another option that some offer is "Encrypting Downloads", which simply encodes your data stream. This is useful if your ISP blocks bittorrent traffic (which some have been doing, assuming it all is an AUP violation).
Another piece of software you may want to look at is Peer Guardian 2. Peer Guardian blocks known "bad hosts" which upload dummy/bad data, or tracks your usage for malicious purposes. This also includes such organizations such as the MPAA/RIAA.
Please note that we do not condone internet piracy in any way, however we do advocate user privacy on networks.