There are probably dozens of ways of finding agents to query. When I first started thinking of writing as a career, many, many years ago, the only way I knew was Writer's Marker, an annually published book that was probably out of date before it hit the shelves. I put my writing aside for a decade (or two) for my career and raising kids. In the meantime, the world moved on!
The advent of the Internet and blogging has drastically changed the availability of information and the timeliness of it. Hundreds of agents are at your fingertips, if you know how to find them.
The following is a list of websites that offer access to names of agents, including what they represent and, in some cases, personal remarks by others who have queried them. Some require registration but all are free, at least to some extent.
Association of Authors' Representatives (AAR)
Writer's Free Reference
326 Fiction Literary Agents
Preditors and Editors
I'm sure every writer has their own way of choosing who to query, but I'll give you my quick rundown, which is thorough but time-consuming.
I keep an Excel spreadsheet with a list of the agents and their agencies. It's important to have both because I want to make sure I'm not querying two agents at the same agency at the same time, generally considered a no-no. I may write down several agents from a single agency, and then query them one at a time. I have columns for the date I query, what materials I send (chapters or pages, synopsis, marketing, in general whatever that particular agent requests). I also have a column for the date of reply and what the response is, and a place to jot notes that might be pertinent, including if I choose, in my research not to query that agent. That way I know I already did the research and decided not to query them for some reason and I don't repeat all the research a week later forgetting about it.
For example, I've come across several agents that look like a perfect fit... except they say they don't rep children in peril. My main character's daughter is fighting off death. After coming across the same name several times and thinking, "Why isn't she on my list? She's perfect!" I find that nugget that says in small letters what I keep forgetting. Now my list tells me that I know about her and have ruled her out for this reason.
I started with Query Tracker because it is a great organizational tool. I punched in what kind of fiction I was writing and it generated a very long list of possible agents for me to add to my own personal list. I go through the list name by name. One of the great things about Query Tracker is that it also has links on each agent page for their AgentQuery Page and their Publishers Marketplace page, as well as the Preditors and Editors and their agency home page if they have one. It's one stop shopping! I can do a ton of research right off this page, as well as see comments other writer's have written about them.
If they look like a good match, I'll go ahead and mark them as a possible on my Query Tracker list and on the Excel spreadsheet. Now I have two lists going. The reason is because Query Tracker offers valuable options and information I come back to time after time, but it's incomplete. I often get names from other places as well - agents that go on my Excel spreadsheet but are not included on Query Tracker.
When I have a good size list, enough to really begin the process, I go down my list one by one, Googling the agent names to find interviews, comments, authors they represent, blogs... anything that will give me a better idea of what they are looking for and how I might fit into their client list.
It's not uncommon for me to have six windows open on my computer (thank you Mac!). By the time I send the query out, I'm confident the agent I'm sending it to is reputable and a reasonable fit.
It's not really important, I suppose, how I go about the process. You will find your own rhythm, your own way of creating your list of dream agents. If you find better resources, let me know and I'll add them here.
It's a daunting process, but you don't have to do it alone! Many of these websites offer the chance for writers to interact with each other, exchange information and recommendations and lessons learned, as well as encouragement. Sometimes agents even get involved with them, stopping by to explain a problem that seems to crop up or update what they are looking for.
My advice is not to pick one website and stick solely with that one. Research widely, query widely, hope hugely!