Select your three best screenplays. If you are wanting a screenwriting agent, it's assumed that you have several scripts that you believe to be "great." Make sure they are indeed just that. The best test is to have several people from all walks of life read your material. If all your readers respond to one particular script with the phrase, "I love it," then that script is in the realm of greatness. Choose three screenplays that live in this realm.
Submit your three great scripts to the Nicholl Fellowships in Screenwriting competition. This competition has launched several screenwriters' careers since it was founded in 1986 by the Academy of Motion Picture Arts and Sciences. Over 6,000 scripts are submitted a year, which is why you'll want to submit three and raise the probability of placement. The early entry fee is $30 per script, and the late entry fee is $45. Once the competition results are officially announced, finalists, semifinalists and quarterfinalists receive waves of emails from agents.
Research your interested agents before you respond to their queries. The goal is to find an agent that fits you and your material. Find out what agency your potential agent works for and whom she currently represents. This will not only give you an idea of what this agency or person is about, but also the kind of material she tends to sell. Find one that is interested in your type of screenplays. Not only will she be more likely to sign you, but it will give longevity to your potential partnership.
Prep your material before responding. Most agent emails will request your script or scripts that placed in the Nicholl competition. Once you send this material, they will read it, then ask for more material. If you don't have more scripts at the ready, most agents will quickly lose interest in you. This is where your other great screenplays (even if they did not place in the Nicholl) come in. Send these.
Have several more screenplay ideas on the brain. After the agent has read all your material, and he gets back to you, you're practically in business. Before offering to sign you, the agent will ask, "What other projects do you have in development?" Have several. Be able to pitch the concepts, stories, and characters of these fetal works. This will seal the deal. With your existing material, professionalism, and a seemingly endless wealth of mental material, an agent would be daffy not to sign you.