So, you have a copy of Literary Marketplace or Writer's Guide to Book Editors, Publishers and Literary Agents, and you have girded yourself for contacting the agents you have marked on your list.
Your checklist should have been compiled very carefully. For reasons that are explained at length on a number of valuable internet sites, don't include agents who ask for a reading fee: as a general rule, they are not interested in your book, but in your pocketbook, instead. Do include agents who want (and sell) books in your genre. DON'T do what I did, once, and send a proposal for a collection of travel stories to an outfit that specializes in cookery books! (True story, and I still haven't worked out how it happened.) If you write in a specialist nonfiction area, it is a good idea to look through the acknowledgements section of a number of books on the same topic, as authors generally thank their agents, which will give you useful names. Otherwise, go through the agents directory in the handbook you have bought, and check those who seem to like your kind of book.
Next, the query letter. Query letters for agent-hunting are the same as query letters for publisher-hunting, as the same rules and format apply. However, while you (or your agent) can approach a publisher with an idea for a book that is yet to be written, when approaching an agent, it is a good idea to have the book written already. Unless, of course, you have established a good record for meeting deadlines.
I believe emails are acceptable these days, but proof a post very, very carefully before sending it out. If you write a letter, put it on good stationery. Whatever way you do it, make it compelling. It's a sales pitch for your work, and your agent (when you find one) will use it to make his or her own pitch to chosen publishers. Jeff Herman's fine chapter on writing a query letter is an excellent guide.
Keep it short, keep to the point, keep it positive. Include your track record in the publishing line -- everything and anything that helps sell your idea, including editing work for your student newspaper, and scholarly papers to academic journals, if relevant to your topic.
And here, as a sample that might be useful for guidance, is the query letter written for Tupaia, Captain Cook's Polynesian Navigator. (I have a wonderful agent, and a good query letter helps to let her know what kind of project I have in mind.)
Dear [name of the agent, and make sure you get it right]
I am planning to write the biography of Tupaia, who was Captain James Cook's Polynesian navigator on the Endeavour. I won grants from CreativeNewZealand and the Stout Trust to research this book and will be traveling to the States and the UK late this summer to continue that work. [This is the moment for you to mention your publishing record, if you have one, but keep it short.]
Tupaia, a gifted linguist, a brilliant orator, and a most devious politician, could aptly be called the Machiavelli of Tahiti. Tupaia, being highly skilled in astronomy, navigation, and meteorology, and an expert in the geography of the Pacific, was able to name directional stars and predict landfalls and weather. Though, like all Polynesians, he had no previous knowledge of writing or mapmaking, Tupaia drew a chart of the Pacific that encompassed every major group in Polynesia and extended more than 2,500 miles from the Marquesas to Rotuma and Fiji.
He was also the ship's translator, able to communicate with all the Polynesian people they met, including New Zealand Maori. As a man of high social ranking, Tupaia performed as an able intermediary, interpreting local rituals and ceremonies. Joseph Banks, the botanist with the expedition, like Captain Cook, is famous for his detailed, perceptive descriptions of the manners and customs of the Polynesian people. Much of the credit for this belongs to Tupaia. Not only did Tupaia become one of the ship's important artists, drawing lively pictures to illustrate what he described, but he could justly be called the Pacific's first anthropologist.
Despite all this, Tupaia has never been part of the popular Captain Cook legend. This is largely because he died of complications from scurvy seven months before the ship arrived home. Once he was gone, his accomplishments were easily forgotten--indeed, by removing Tupaia from the story, what the Europeans had achieved seemed all the greater. James Cook, who could well have resented the fact that Tupaia had been hailed as the "admiral" of the expedition by his fellow Polynesians (the Maori people called the Endeavour "Tupaia's ship"), apparently found it easy to dismiss his memory with a brief, unflattering obituary in his journal. When Cook received his medal from the Royal Society--for his great achievement in bringing the ship home without losing a single man to scurvy!--Tupaia's name went unmentioned.
George Forster, a scientist who sailed with Cook on a later voyage, called Tupaia "an extraordinary genius." No book until the one I plan to write, however, has been devoted entirely to Tupaia.
Let me know if I may send you the proposal. I'll look forward to hearing from you.
And that's it -- or something like it. If you send the query out by post, include a return envelope, postage paid. To save time, it is perfectly acceptable to query a number of agents at once. If you are lucky enough to get a number of requests for your proposal, you must say when you send them out that this is a multiple submission. Indeed, the fact that you have received interest from other quarters should be an incentive.
HINTS ABOUT THE PROPOSAL TO COME.