Using a magnet link is as simple as clicking the link on a web page. If you have a magnet link capable BitTorrent client installed, your web browser should prompt you to open the magnet link in your torrent client. You can also copy and paste the link into BitTorrent clients that have an address bar for that purpose.

If you head to the Pirate Bay now, you'll notice that magnet links are now the default, with the "Get Torrent File" link in parentheses next to it (a link which will disappear in a month or so). Just click on the magnet link, and your browser should automatically open up your default BitTorrent client and start downloading.