Familiarize yourself with script formatting so your script will look professional. The Script Frenzy site listed below has a writer's resource section with instructions on formatting plays, movies and television. Filmscriptwriting.com is another formatting resource. There is a lot of competition for production. Submitting an amateurish script can knock you out of the running. Learn proper stage direction and characterization to increase your chances.
Read scripts by other authors to see what a play should look like. Scripts are available in bookstores and libraries, or go to an online source such as simplyscripts.com where you can read many genres of scripts. Determine, based on your story's content, how many acts your play should be. Write your play. Be sure to proofread several times or have a friend read it for you. Be sure that your submission is error-free in order to be taken seriously. Read the script aloud to see if it sounds like genuine conversation.
Look for markets for your play. Use one of the many resources available online or at the library to see where your play will fit best. Withoutabox.com lists contests and festivals all over the country. Writer's Market is a book published yearly that lists markets for scripts. Script Magazine and Writers Digest Magazine contain market information, articles and tips about scriptwriting.
Good beginner markets include community theatre or high school or college productions. See locally produced plays to determine their styles and to familiarize yourself with the local theatre community. These frequently are non-paying markets, but they can build your credentials to make it easier to break into paying markets. Look to local media for "Calls for Work" and visit local theatre websites frequently.
Another source of income from scriptwriting is publication. Submit your full length play or collection of one-act plays to a script publisher.Top Script publishers include Dramatist's Play Service, Playscripts Inc. and Samuel French. Study their submission guidelines carefully.