Open a web browser such as Internet Explorer or Mozilla Firefox.
If you know which channel broadcasts your show normally, you can go directly to their website. For example,
www.nbc.com (click on "Watch Video")
www.cbs.com (click on "Video" or "Hd Videos")
www.abc.com (click on "Free Episodes")
www.usanetwork.com (click on "Video")
When you find and select the episode of the TV show you want to watch, you may be asked to install a video player by some of these sites. Go ahead and install it if you want to watch the show.
If the show you are looking for is not in one of the above mentioned websites, go to www.Hulu.com
In addition to having current TV show episodes online for free, Hulu also has older shows and lots of movies for free that you can watch.
www.TV.com is another website that has some free TV shows.
Sometimes, you can find clips of interesting shows on www.youtube.com, so don't forget to check that out as well.