Study and perfect your craft. Unless you have extreme youth on your side, agents typically want trained actors, directors, and writers. Acting schools and master's of fine arts programs not only teach craft but they often offer access to agents on guest panels, lectures or showcases. Many of the instructors also work in the industry and offer recommendations or general advice. Studying in a film or theater program not only gives you access to working professionals, but also builds your resume.
Create your own work. Writers can sit down at their laptop and bang out a script, but actors and directors can create their own work, as well. Digital film making gives amateurs a relatively cheap medium to showcase their talents. The videos can be put up online. A million hits can show a potential agent you can attract an audience. Submit the film to contests that offer winners access to agents. Put on theatrical productions and invite prospective agents to attend. Big agents probably won't show up, but sometimes their assistants will, especially if they're trying to build their own roster.
Attend a conference where agents will be in attendance. Most charge a fee, but they can offer an opportunity to pitch an agent your movie idea or script. Others allow actors to audition for prospective agents. Even if the agent doesn't take you on as a client right there, you can always send future projects and remind her when you met.
Research and gather agents specializing in your talents. You can find directories of movie and Broadway agents at the bookstore or online. Bigger agencies typically expect a high quality body of work under your belt, unless you're a child actor, so while you can seek representation from larger agencies, you should also seek out boutiques, which might be more open to fresh talent. Research the submission guidelines for the agent, which can often be found on the agency website.
Gather your materials to create packets to send out to the agents. For actors, you need pictures, resume and a demo reel of your work. Hire a professional editor to help put together an exciting cut to entice the agent. This might be a short film you've starred in or video of a stage production. Writers need both a resume and a full-length sample script. Directors should put together a reel of the films they've shot. Include a cover letter introducing yourself, and mention any recommendations you might have gotten or if you met the agent.