Make a list of 10-15 agents who represent writers in the genre you are trying to break into. There are a variety of books in the market as well as Internet databases to help you find the right agents to suit your script.
Use a standard business letter writing format to draft your letter. Put the name and address of the agent/company at the top right-hand corner of the page. Use 1-inch margins and 12 point font in all of your letters.
Begin the letter with an appropriate greeting such as "Dear Ms. or Mr..." Start by stating precisely the reason you are writing, such as "I am a screenwriter with various screenplays I would like to submit for your consideration for representation."
Continue the letter by listing the various screenplays you have written and very briefly (one or two sentences) telling the agent what the screenplays are about. Tell the agent the genre of the film and the overall themes as succinctly as possible. This portion of the letter should make up the bulk of your query.
State any awards, previous publications, qualifications or screenwriting contests or options you have secured to help make your query more attractive, however don't spend too long on this section, your work should speak for itself. Ask the agent if he is interested in reading any of your scripts to contact you directly (providing appropriate contact information) and you will promptly send him your work.
Print the letter and address the envelope. Ensure that you use the proper postage. Consider sending it priority mail if you want to guarantee the letter's arrival at its proper destination.