WRITE A SOLID SCRIPT
The first step in marketing a television script is ensuring you have a script that is marketable. Is the script written well? Is the story appealing? Is it written using proper screenplay format? Are the characters realistic, entertaining and engaging? You must ensure that the script is ready to go. For a television script this should be a 45-60 minute "pilot" script.
WRITE A SERIES BIBLE FOR A NEW SERIES
If your script is for an existing television show then proceed to step 3. Otherwise, if it is for a new television series you need to write a SERIES BIBLE. What is a series bible? A series bible is essentially a large overview of the proposed series. It will cover characters / thematic issues / story and character arcs / setting and practically anything else important for maintaining series cohesion over a long period of time. Look around on the internet and you will find a few examples which you can use as guidelines for writing your own.
BEGIN MARKETING
Okay, at this point you have a solid script as well as the series bible. Now you need to get it in front of people. For a new writer you will pursue three angles of approach: 1) Personal contacts (friends, friends of friends hoping to find a connection to someone in the movie business) 2) Agents (Use any of the agency guides to find reputable agents to send the script to) 3) Producers/Studios (These are usually found in the same type of books as you will find agency contacts).
EVALUATE RESPONSES
It it important that you evaluate the reception your script is getting from people. You can safely ignore one individual opinion, but if 5 people tell you the story/series doesn't work then you have a problem. The same applies to characters/plot etc. If you need to rewrite something then you need to pay attention and do it before you send it out again.
IGNORE REJECTION / REPEAT MARKETING
The marketing process can go on forever. For a serious writer the best thing to do is to start working on another script and set a goal of "X" number of contacts each month for previous scripts. Thus, you might set a goal to send out 5 query letters or make 5 pitches on this television script while you work on a new screeplay.