Search for sites devoted your show. Many fan websites offer links to online video for the show, as well as episode information and recaps. If there is up-to-date information you need, these sites are the place to find it.
For shows that are currently airing, check the websites of the networks. Most non-cable networks provide Internet access to the most recent episodes of their programs.
Look for your show on websites like hulu.com, which air authorized videos of many different TV shows. Both on-air shows and older shows can be available via such sites, although most of the newer shows only have a few recent episodes.
It is possible to purchase episodes of TV shows online. iTunes is one of the most popular sources for current television shows, but you can also purchase online TV shows from sites like Amazon.com.
Use sites that offer television shows streamed live from stations around the world. This is an especially good way to watch TV not generally shown in the country where you live.
If you can't find your show any other way, do a search for free TV websites. Many of these sites are unauthorized, and few offer high-quality video. They do, however, provide links to virtually every TV show.