You've written the book, you've spent hours perfecting your query and synopsis, and now the time has come to get your baby out into the world. Where do you start? There are, literally, hundreds of literary agents out there. How can you possibly know who they are, what they like, and which one would be the best fit for your work?
The best place to start is by making your own personal agent "wish list", i.e. what factors are the most important to you in a working relationship. Remember, your relationship with your agent is a partnership akin to a marriage. You have to be able to feel comfortable to approach them with questions and issues, there needs to be clear communication, and that person has to "get" you and your work. Are you more comfortable working with a man or a woman? Huge established agency or a smaller boutique agency with a smaller client list? A newer agent or someone who has more experience? Someone who communicates to you every step of the way or someone who just checks in when there's something important to say? Based in New York or based somewhere else? (By the way, the latter point does not seem to matter much these days with the advent of the internet, Skype and whatnot - they all are well connected to the primarily New York-based publishing houses.) Written contract or verbal agreement? Only you can answer these questions as to what works best for you, and will help you hone in on select people as you begin your search.
The next step is to become familiar with several key websites that are a tremendous asset in helping research what each agent is looking for. Hands down, the best one I've found is Literary Rambles, which is literally a one-stop shop for finding the low-down on some of the top agents in the business. The site has specific submission guidelines for each agent, their interests as far as requested materials, and an abundance of links to further research anyone who catches your eye. You can branch off and read interviews on blogs, or see their listings on Publishers Marketplace, and so on.
Also excellent are sites like AgentQuery.com, which allows you to perform searches in a specific genre and also has information like comments from other writers, response times and request percentages, contact information, and much more. This site will also tell you if the agent likes to see queries by email or snail mail.
There are also many invaluable blogs, which I have mentioned in previous posts, and books like Writers Market and Jeff Herman's Guide to Book Publishers, Editors and Literary Agents. These books are updated annually because editors and agents move around a lot, so it is always best to check the agency's website directly to make sure that particular agent is still there. Writer's Digest also has an online component with the most current listings if you purchase the deluxe edition. They also have a smaller resource guide that is specific just for literary agents, which can be found here.
Start small and send out queries to just a few at a time. Hopefully, someone bites with interest right away, but if not, you can take the feedback you get to help you tweak the query or hone your focus differently. For example,Agent A that works for mega-huge agency that you'd sell your first-born to work with may state specifically she loves paranormal and sci fi and you're sending her your contemporary romance. Show them you've done your homework. Know who they represent, especially if they rep writers similar to how you write.
And most of all, have patience. This process takes a loooooong time, unless you're one of the super lucky ones who gets an agent right out of the gate, but remember, they are the exception, not the rule, so don't feel like giving up if it doesn't happen on the timetable you've envisioned. Good luck!