I got this question recently:
“I wrote an episode for a television show I like, and have ideas for more. I’ve read your posts on TV writing, but they seem to be mostly about developing a series. What I’m wondering is how I might best go about approaching the producers/creators of the show to ask them if they’re interested in reading my episodes. When I’m done writing and I send them a query letter, would a few sentences per episode be sufficient? Or longer?”
It might be wise to take a step back and understand why it’s a good idea to write spec scripts for existing shows. What you’re trying to do is create a cache of high quality specs that you can use as writing samples. So if you’re going to write a bunch of t.v. specs you should write them based on a variety of different shows. What you’re really hoping for is to submit these specs to agents and managers who will represent you and submit them as writing samples to similar shows to get you staffed on one of those shows. So it’s important to be able to show you can write for many different, although similar, shows.
While it is possible to sell spec scripts to existing shows, it’s very difficult for a variety of reasons. Often times the people running television shows simply have egos that are too large to accept scripts from outsiders. In addition, there are often lots of subtle things that an outside writer simply would never understand about the show like long term story and character arcs.
To answer your question, though, in most cases the actual production company that produces a show will be listed in the Hollywood Creative Directory or on IMDB Pro. Look them up, find the name of the show runner or head writer, and submit a query letter to them. If you have completed scripts for many episodes you might as well pitch a log line for each episode as you never know which one might interest them. Again, I want to emphasize that this is going to be a real uphill battle!
Next, I would break out the Hollywood Creative Directory agents and managers edition and start submitting query letters to them, too, as this is really your best shot at becoming a television writer.