Starting with torrents is very easy and only requires downloading and installing a torrent client. You will also need to have decent Internet connection to be able to download files in reasonable time frames. If you are unsure about your internet speed you can check your internet speed at http://the-online-world.com/Internet-Connections-speed-bandwidth-meter .
Some very common BitTorrent clients are utorrent, Azureus, BitSpirit. Many of these clients are available for free. Once you have installed your torrent client you can change various settings about bandwidth, connection and UI etc. Once done with setting up the torrent client, just browse for a file you are looking for in a torrent search engine like isohunt. Downlaod the torrent file and run it in the client. The file download will then start automatically. It is better to be careful with using torrent search engines. A lot of search engines have pornographic advertisements on their website. I prefer isohunt since it is clean and easy to use.
Torrent file sharing has its share of drawbacks. One is the huge amount of network traffic that it consists. Also, torrents have become a hub of downloading pirated and copyrighted materials. When you download torrents of a file, the onus is on you to make sure you are not downloading copyrighted material. Several countries have started punishing peers who have indulged in such behaviour.