There are a lot of tv shows and movies that are available for free on the internet on various tv network's channels and on sites like hulu.com and fancast.com . I like fancast.com the best because the viewing window is the largest. Most sites will let you enlarge the window to fullscreen, which is whatever size your monitor is. Not every show is available online and not every episode of every show is available. The CSI shows are available for a week or two after they air, starting the next day, on cbs.com. None of the Law and Order shows are available online. It takes some time and exploration to find out which shows are online, and how long they are available online. Bones is available for several weeks online, as are many Fox shows. TNT has a few episodes of their current shows available most of the time. I found a lot of programs by going to each tv network's site and looking around. Most network sites have a tab for video somewhere on the home page. Otherwise if you are curious about a show you can go to the show's website.
I do not know how to put this on your regular tv. I do it because we only have satellite in one room, so if the kids are watching something I don't like, or if I want to see something that might disturb thank you or husband (neither likes the cop shows like CSI much) I watch it in another room.
I don't know about the pay services for online watching. I have looked at a few and most seem to charge for stuff that is available free. For shows like Law and Order I have had good luck finding used seasons on DVD at affordable prices. That way I can watch them on any computer or on the tv.
Check out what reviews say before you sign up for a pay service for internet tv.