Depending on whether you are an actor, writer or director, the process for getting an agent is a bit different for each vocation. But no matter what you wish to be, the trick to getting an agent however, is that you usually need to make most of the effort.
How to Get a Talent Agent: Actors
For actors, the type of agent you need is called a talent agent. That might seem obvious, but there are a number of different types of talent agents depending on what type of work you're looking for.
You want to start by finding someone who specializes in the area that you're hoping to break into. A talent agent that specializes in film is very different from the one who specializes in commercials. So, begin by determining which direction is best suited to you.
Talent agents usually find their clients in one of three ways: 1) they are referrals from other people; 2) they are people they sought out (most often established actors that were "stolen" from other agencies); or 3) by "discovering" them through a talent showcase, student film or other completed work.
Does this mean that you won't ever be discovered by working as a waitress at a Hollywood industry hangout? No, but your chances are markedly decreased if this is the only effort you make.
Too many actors think that an agent will choose to represent them, simply because they have an amazing headshot. True, a good headshot might give you the slightest edge toward getting a meeting, but more often than not, it ends up in the circular file (the trash).
NOTE: One quick note about headshots -- you want to be sure that no matter what, you look as close to your headshot as possible. If you've gained or lost weight, changed your hair style, or simply aged a few years, nothing will turn off a casting agent faster than an inaccurate photo representation of you. Pay the extra money and update them as you need to.
The trick to getting a good talent agent is to be sure that you put yourself in a place to get discovered. That means, find work on your own. That could mean anything from doing talent showcases to student films to whatever else you can find. If you live in Los Angeles or New York (and even if you don't), you should subscribe to Back Stage West (either the magazine or the website), as this is an excellent resource for aspiring actors to find student and low budget movies that are casting and are more likely to consider "green" actors.
You should also check out Craigslist.com. It's surprising how many low budget films advertise there looking for casting potentials. Be careful choosing this route however, as a lot of low-lifes post seemingly legitimate ads only to reveal later that their only objective is to get you to take off your clothes.
NOTE: Be aware of anyone who wants to charge you money for their "representation" services. Agents rep their clients for free and only get paid when they get their clients work. Stay as far away from these types as you can.
How to Get a Literary Agent: Writers
With writing, again it's very important that you first determine what type of writing you wish to do. Are you planning on becoming a feature writer (movies), television writer or a novelist? (If you are in fact planning on becoming a novelist, know that much of what follows will not apply to you. This section will focus on film and TV writers.)
Once you've decided what type of writing you wish to specialize in, now you can start the process of getting an agent.
The first thing you need to have is some sort of written material. After all, you can't really call yourself a writer if you don't have a body of work that represents what you're capable of. So, be sure to have either a spec script (or two) if you wish to be a TV writer or a feature spec, if you wish to write for film.
Once you have these materials in hand, you can't just blindly submit them to agencies and then hope that they'll read your script. This is when your networking skills become key.
You will want to be sure to let all of your friends and co-workers know that you hope to break in to Hollywood as a writer and that you're in the market for an agent. Chances are someone will know someone who will know someone who will know someone that can get your material in front of an agent.
Literary agents are, for the most part, pretty intelligent people who are always looking for good material written by good writers. After all, they all want to take credit for finding the next David E. Kelly or Aaron Sorkin -- and who's to say that's not you? If they read your stuff and like it, chances are they'll seek you out. The hard part is getting your material in front of these people. So, that means you have to network, network, network and network some more.
NOTE: One thing you need to be aware of however is that you will likely just have ONE chance to make an impression on an agent. They are very busy people who aren't likely to give writers a couple of chances to impress them. So, only submit your material when it's at its very best. That means everything from making sure you dialogue, story structure and characters are top notch, to making sure you have proofread your script for typos (as they can get quite annoyng. See what I mean?)
Another thing -- don't spend a lot of time on your cover. You material should look like a script. Plain, white, three hole paper bound with brass script brands. Don't bind it, put a fancy cover on it, and never put any other information on it other than the title, author (hopefully you), and your contact information. Anything else and people reading it will know you're an amateur.