I cover this topic in depth, including my own thoughts about who needs an agent and who doesn't, whenever I teach one of my children's writing courses. I do it even when the class isn't really "about" the business of writing because the topic is just that popular.
The short answer to the question — assuming that you are serious about writing, that you are writing and have at least one finished manuscript in hand — is:
Do your research.
You can handle this, I promise. The process of finding an agent is similar to the one you'd use to find any other service provider. When you need a specialized doctor or attorney or building contractor (and bless you if you need any of those, btw), you start by researching who handles the type of issue you need handled. If you write YA sci-fi novels, then look for agents who represent YA sci-fi novels.
Once you've identified several likely candidates, try to find out more about the books and authors they've worked with. (Specific information will lead you to a better match.) Still comfortable with your list? Narrow it or don't. Then start getting in touch. Introduce yourself in whatever manner the agent prefers: email, snail mail; query only, query plus writing sample.
Each agent will tell you whether she is interested in working with you. The tough part about this stage is that some agents will not be interested. That may seem like they have all the power, but wouldn't you rather have your work represented by someone who loves your work? Sometimes a rejection is based solely on the fact that an agent deems a work wrong for the current market, or maybe she just doesn't work with your specific type of story because s/he doesn't have great contacts with the publishers likely to want it. Rejection from an agent does not necessarily reflect on the quality of your work. It may mean nothing more than you need to keep looking.
Remember, too, that you don't have to work with someone you're not excited about just because she wants to work with you. Assuming the agent sells your work for you, you will pay her for that service. In the end an agent works for you.
For more information, take a peek at these resources.
A huge agent database ripe for the searching.
Association of Authors’ Representatives
Members of this professional association agree to a set of business and publishing ethics.
Children’s Writer’s & Illustrator’s Market
This annual market listing for U.S. children’s publishers can help you determine which publishers are the best fit for your submission. Each publisher notes whether they accept agented or unagented works (or both).
Guide to Literary Agents Blog
The editor of the annual agent directory Guide to Literary Agents blogs about agency and other industry news.
Preditors & Editors
You can search this listing of agents to see which ones get high or low marks from the site and its visitors.
This is the international organization for professional children’s writers and illustrators. They have many thousands of members, chapters all over the world, local and national conferences, relevant-to-you publications, and an online discussion forum.
The online version of the popular annual directory Writer's Market. It contains market listings available in the Children's Writer's and Illustrator's Market. Features agent Q&As.