This is an excellent question, and one I get asked often. There are many ways to go about this, and to do this research thoroughly, the right way, will take much time and effort. That said, here are three quick ways to help start your search:
1) Visit www.publishersmarketplace.com and click “Deals.” Under “Browse deals” set the drop-down tab for Year to 2009 (also do this search for 2008 and 2007). Set the “categories” drop-down tab to the genre of your work (for example, “Fiction/Thriller”) and click Browse. I just tried it in the “Thriller” genre, and it returned 53 deals for 2009 and 116 more for 2008, totalling 169 reported deals for just the last year and a half. Scan through each and you will find the name of the agent who made the deal.
2) Visit www.publishersmarketplace.com and click “Top Dealmakers.” Set the Dealmaker drop-down tab to “Agents” and set the Deals category to the genre of your work (for example, Fiction/Thriller). I just did it and it returned information on the top 100 agents who recently made deals in the genre—and even sorted them in order of the number of deals.
3) Visit http://books.google.com/ and in the search tab type the key word “Acknowledgments,” and then (separately) type in the name of relevant authors and books in your genre. It may bring up the acknowledgments pages of relevant books, and these may mention the names of the agents.
As I said, all of this is just the tip of the iceberg. There are many more ways to go about this (I discuss this topic at length in my book, How to Land and Keep a Literary Agent). Also keep in mind that, aside from the genre, there are many additional factors you must consider in order to properly evaluate whether an agent is the right one for your work.