The initial moves which see an author being signed up by an agent are usually - though not always - made by the author, not the agent. For this reason you should first think about what sort of agent you want (see yesterday's post) and then do some research to find them.
I've heard of this research being portrayed as an onerous chore, but in my opinion it's just an extension of being part of the publishing world that you want to join. You're probably reading novels you'd like to have written and magazines about writing, going to writing classes and conferences any way, attending literary festivals and getting involved online anyway. It doesn't seem particularly onerous to keep your eyes peeled for an agent you'd like to be represented by while you're doing all those things.
Because that's where you do your research. Agents speak at conferences and literary festivals. Their authors mention them in the acknowledgments. They are quoted in magazines. Writing class members will discuss agents they've approached and what the response was. Look at their websites for their biographies to get an idea of their background in writing or Google for any interviews they've given - a brief biog is usually included. Ask online groups. Follow agents and publishers on Twitter and Facebook, subscribe to news e-bulletins from The Bookseller and book2book, get out there!
I didn't have any contacts at all in publishing when I started but I still managed to meet lots of agents at various writing events such as literary festivals, conferences and writing association parties. And a couple of years ago I set myself a challenge to find the background of 15 randomly selected editors, just to see how easy it was. Within 3 hours of Googling, I'd got the details of all but 2.
It's not that difficult, you've just got to do it because you don't want to waste your time and energy asking for representation from someone you actually don't want to represent you.