I highly recommend this book, Guide To Literary Agents, to anyone with a completed manuscript and looking to enter the publishing world.
Now whether you buy it, borrow it from the library, or sit in a big chair at the bookstore and take notes is up to you.
But what you will find is a comprehensive guide to hundreds of official literary agents, their names, what categories of book projects they will consider, their comission, a list of clients and books they've represented, and how they like to receive queries. (Official agents don't charge you anything up front... they only receive money once your project has sold. Don't get taken in by con artists masking as agents, and there are quite a few!)
There are also practical how to's included -- examples of query letters, interviews with agents on the business, and guides on how to be a good client.
It is important to get the latest edition of the guide, as agents switch agencies, go off on their own, move, or retire.
Another way to seek out a literary agent. Make sure you read the acknowledgements pages of your favorite books. Once you find the agent name, do a quick online search or check the Literary Guide. Generally, authors thank their agent. And chances are if you liked the book, you'll like the agent... or the agent will like your project if it's similar.
Or, if you're enrolled in a creative writing class, a writing group, or attend writer retreats/conferences, you'll also have an opportunity to network and meet agents personally.
The thing is this. These days if you're looking to be traditionally published, you have to have an agent. They are the one's who pitch your project to publishers to consider. They serve as your communication liaison with the publisher/editor.
Getting an agent can be very time consuming and challenging. Once you query, you'll receive a good number of rejections as well as a good number of requests for your material. Be prepared to wait. Be prepared for rejection. Have patience. It's all about the right fit... and the work being ready for publication. My writing teachers and groups have always advised, "Don't send out your work too early. Make sure it's in the best shape possible." I offer the same advice.
But be sure your book is complete (meaning it's finished), grammatically correct, story in the best shape possible, and that you're not sending in your first draft. A first draft, while it may be your most "authentic" voice, isn't usually the best draft.
The hunt for a literary agent can be long and arduous. And once you have one, it's no guarantee that you'll be published. It just makes the journey a bit easier.
We can talk about agent expectations down the line.