In general, you should use "the TV" or "a TV" in the same way that you would use "the" and "a" with other countable nouns, if you are talking about a TV as a physical object. If you're using the word "TV" to mean "TV programs" (movies, shows, commercials, or anything else that is aired on television), then you don't use "the" or "a."
"I'm watching TV" means "I'm watching the shows/programs that are playing on TV." It doesn't mean that you're watching the physical object. Instead, you're watching the images that are playing.
"There is a new movie on TV." Again, the movie is not sitting physically on top of the actual, physical television set. The movie is playing "on" television. You don't need "the" or "a."
"I just bought a new TV. The TV cost a hundred dollars." Here, you are talking about the actual object. You bought an electronic device, a TV. You need to use "a" or "the."
So if you want to say that there is a real, physical flower pot sitting on top of your TV set, you need to say "There is a flower pot on /the/ TV." (Usually we would say "on top of the TV," just to be perfectly clear.) If you want to say that your favorite show is playing right now, you would say "My favorite show is /on/ TV right now." In this case, you don't need to use "the."