Prepare a killer resume. List your legitimate theatrical credits, the size of the roles, acting training, other credentials. Take time to write and format it well (first appearances are everything, and how you come across on paper makes an impact). It's helpful to include a demo reel. Most important: don't lie, fudge, or plump up your credits. Agents can see through such tactics, and will close the door before you've had a chance to open it.
Get a referral from an actor to an agent you're interested in. As is true in all businesses, personal recommendations can open doors.
Get a great headshot. Ask other actors whose head shots you like who they used as a photographer. If you take an acting workshop from a casting director (this is excellent training to list on your resume, by the way), ask the casting director who they recommend. Then interview the recommended photographers, pick one you're comfortable with, and set up a photography session.
Make a list of recommended agents. Ask fellow actors and casting directors who they recommend. Ensure that the agent is licensed and bonded with the state and franchised by the various unions and guilds (check the Association of Talent Agents at http://www.agentassociation.com/ and look up the agent in the Screen Actors Guild database http://www.sag.org/content/find-agent).
Mail your resume and demo reel to the agents. Put your cover letter (keep it simple but engaging), head shot, resume (stapled to the back of the head shot), and demo reel in a manilla envelope and mail one to each agent.
Unless you're invited to, don't do the following because you'll look unprofessional and sabotage your chances:
Don't call the agent.
Don't email the agent.
Don't show up at the agent's office and ask for a meeting.
You got an interview with a great agent, now what? It's time to shine. Remember, it's an interview so dress and act appropriately, but also be yourself. These are people who will be selling you, so give them something they want to sell. Look great, be appropriately conversational, be prepared to present a monologue should they ask. If you're chatting it up with an agent and his/her associates for over thirty minutes, you're doing well!
Some no-nos:
Don't be negative. An agent will be turned off by complaints, bad moods, or any other dark clouds hanging over your head. If you've had a bad day, park it outside.
Don't belittle yourself in any way. Maybe you complain about your weight, hair, or significant other to your pals, but don't do it to a prospective agent.
Don't talk about past bad agents. If you've had an agent or two before, keep that history to yourself. This is a job interview, not a dish session.
You've signed with a great theatrical agent, now what? Keep up the momentum of your career. Continue taking acting classes with reputable teachers; learn the business of the industry so you can intelligently discuss contracts with your agent; attend industry events; perform in showcases; stay current with theatrical news, performances, TV and film; research actors, directors, productions you like.
After all, signing with a great theatrical agent is the beginning of the next stage of your career, so pick up the pace and race for that star!