I download using a system called bittorrent in which you download a small meta file (torrent) which contains all the information a bittorrent program needs to get the files. Here's the wiki entry on bittorrent if you want to know more about it:
http://en.wikipedia.org/wiki/Bit_torrent
I suggest using this bittorrent program though any will be fine:
http://www.bitcomet.com/
After you have a bittorrent program then you can use any number of websites to find the files you want. Here's one that specializes in TV programs:
http://eztvefnet.org/
Some networks, in particular HBO are trying to find, stop and/or sue people downloading shows so I'd use this to protect yourself if you want anything from a cable or pay network:
http://phoenixlabs.org/pg2/
If you've never downloaded video from the internet you probably don't have the video codec required to play it. So when you try to play the video and it give an error, go download the free divx codec here:
http://www.divx.com.
Use this info at your own risk. If you do get caught you'll most likely get a notice from your ISP telling you they received a complaint regarding a certain file. So basically you'll be asked to remove the file and stop doing whatever it was that you got caught doing. You're information normally won't be released to the RIAA or copyright holder on the first offense and normally the copyright holder won't go after you unless you keep doing it.