Once you're able to do this your chances of finding representation explode. However, before I tell you how to do it you must understand that no matter how well you get to know an agent, they are only going to represent you if they love your book. Like your mother taught you, no means no and when an agent says it that means its time to move on, not plead your case. They will not love it more if you can just explain it to them in person. It's your writing you're trying to sell them on, if it didn't convince them in the first place the spoken word certainly won't. Even if an agency lists their phone number on their site you should never call them unless you're invited to or you become a client of theirs.
Once you get to know an agent and think they will be perfect for your work, it's even harder when they say no. This is especially true if you think you'd work well with them. I'm speaking from experience here folks. But, be noble and take it like a pro if it happens. Now that you've been forewarned, on to how to do it:
Look up their agency on the web. If they have a web site it is a huge advantage and a way to at least see how they present themselves and their clients. I love agents who brag about their clients on their website. If they don't have a site and you think they'd still be a good match for you, that doesn't mean you have to give up, you just have to look harder. Check FaceBook and MySpace, see if their agency has a page, or better yet if they personally have one. See if they're on Twitter. Follow them in these areas will give you a huge insight into the way they work and what they like. I've discovered volumes about agents by following them. You might even get lucky enough that they'll follow you too! And of course, there is little I love more than an agent who blogs. They'll tell you practically everything you want to know about their work style and what they like and dislike that way, it's fantastic! Last, but definitely not to be discounted, is attending conferences or writer's retreats and meeting the agent face to face. This one is expensive but remember, it's your future you're investing in. If you're able to go conferences can really get your foot in the door. But if not don't despair, with the world wide web there aren't many obstacles that can't be overcome.
Here are some examples of why I follow people in the industry (ALERT! Query letter advice!): http://blog.writersdigest.com/norules/2009/07/21/5ElementsOfQueryLetters.aspx
And for my dedicated readers here is a continuation of an agent's dislikes in a query: http://www.johnsonliterary.com/blog/2009/7/23/slush-realization-round-up.html