Write a marketable script or pitch. This sounds simplistic and maybe a bit of an overstatement, but in the screenwriting market today, there is an overabundance of every kind of script and idea. To say that the market is saturated would be a huge understatement. You are your own boss. You make your own schedule. And that is exactly what a good writer must have: a regular schedule. If you are serious about writing screenplays as a profession, set aside a chunk of time every day devoted entirely to writing.
Do readings of your script. This kills two birds with one stone. You are able to get the word out about your script by inviting people to read it and experience it in that way. You are also able to hear the words read aloud by a group of people other than yourself, helping you to hear what works and doesn't work in your script.
Register your script with The Writer's Guild of America. You must protect yourself and your ideas. You must also register with the Library of Congress, but it is more expensive. Registering with either is perfectly acceptable, but it is recommended to do it both ways for extra protection.
Enter the script in contests and fellowships.
Submit your idea (and yourself) to literary agents. Do your research, and don't send queries to agents that don't represent screenwriters. It is a waste of your time and theirs. Focus your submissions and make each query letter personal to that agent.
Think outside of the box. This is a tough business to break into. Creative thinking is the only way most people get their films bought or made.