You have to start with a "smart TV" which is one that can be hooked to the internet, or a TV with an HDMI connection that you can hook up an internet device to.
My TV is the latter so I got a Roku box, the Roku III. The Roku gets the internet signal - either directly through a cable or remotely if you have some kind of wireless setup in your house - and passes it on to the TV through the HDMI connection. I had to do a little setup to register the box on my computer but that's a pretty easy process, just follow simple step by step instructions when you turn on the Roku box.
That lets you get Netflix, Amazon, Hulu and a ton of other streaming services. They offer new and old TV programs and a bunch of movies. Netflix is all inclusive for one monthly charge, about $7.99 I think. Amazon Prime also has a monthly charge but it only offers some stuff free with that, the rest is pay as you go, like $1.99 per episode for the latest episodes of current TV programs. The others are a mix of free and pay as you go although a lot of the "free" ones stick commercials in the middle of the movies - Netflix doesn't do that btw.
I cancelled my cable TV subscription several months ago and couldn't be happier. Cable TV had 100 plus stations, 96 of them were garbage and the other 4 only had a few decent programs on them. I was flipping through commercials all the time. With the streaming services you choose what you want to see when you want, stop them in the middle and pick up where you left off etc. You can see current TV programs if you don't mind paying, or just wait until Netflix streams them. I missed the last episode of Walking Dead last year and finally saw it when they added season 5 this past Saturday. I could have paid $1.99 to see it on Amazon Prime long before this but I'm too cheap.