Register with sites such as "agentquery.com," "querytracker.net" and "authoradvance.com" or purchase the latest issue of Writer's Market and look up agents who represent your chosen genre. (Resources 1, 2 and 3) Use the information you find to visit the agency's website, to read an agent's personal blog and to watch them on Twitter.
Make a list of agents you'd like to submit your screenplay to and follow their agency's submission guidelines. Avoid sending out blind queries or querying every agent you can. Focus on the ones that show an interest in your genre and those who are looking for what you enjoy writing. Depending on the agency, you'll need to write a query letter and possibly a one-page synopsis explaining the entire plot of your screenplay before sending them the finished piece.
Send each query letter to one agent at a time and write "Query -- title -- author name" in the subject line of their email. This is to keep your query letter from landing in the spam folder. Paste your query into the content area of the email and only attach files such as a synopsis or the first three scenes when asked. Agents can take anywhere from a day to three months to reply to query letters.
Send out your screenplay once an agent has shown interest in it. Note that a partial read takes less than three months in most cases while having the agent read your entire work can take up to six months.