It's worse than looking for the Holy Grail. Every agent does it different. Some want ONLY snail-mail queries. Some want ONLY e-mail queries, without attachments. If you send an attachment, be prepared. They'll delete you on the spot. And some ... only want your query submitted through their web site application. Some, don't care. Just send the damn thing.
Do you know how difficult it is to get a query, synopsis, and the first three chapters embedded into the body of an email to look nice? You work your butt off to get your query looking pristine and perfect, then your email program displays it all out of whack. So, you spend even more time fixing it on the email. You wonder what it really looks like when it arrives in the agent's Inbox. Do they realize your hard copy is perfectly formatted and isn't all wompy-jawed?
I like snail-mail, personally. You send your perfectly formatted work through the mail, along with a Self-Addressed Stamped Envelope (SASE). Then they send back their accept/reject letter. (Or most of them do.) With email - you're lucky to hear anything. It's way too easy to hit delete and never have to bother with the writer at the other end, whose praying for some kind of response.
Some agents want only the first three pages of your work. Others demand the first 50 pages. Some want sample chapters. For the majority, it's query only! On pain of death you, if send anything else, you're "outta there!" Strike out!
Some agents want stroked. They want to know why you chose them, what books they've sold that you've read, and how you heard about their agency. Others, don't care how you heard about them, they want a well-written query letter, a SASE, and are clear that they are building their client list. But "don't call us, we'll call you," is pretty standard across the board.
A few agents I've researched look really stuffy. Like, "Hey look at me, I'm really something here in my New York City corner office. You'd be damn lucky to get me, baby, so don't bother writing unless you're the next Dan Brown." Some even state that unless you've been published with a major publisher, don't bother to send a query letter.
Then there are others, who go out of their way to visit you at writing conferences in remote parts of the country, like West By God Virginia and even in Vancouver. They dedicate hours to teaching writers what it takes to publish with a major house. Talking long into the night, the agents who attend writing conferences experience meaningful conversations with some writers, while offering tons of encouragement. The writers, in return, always take home with them a sense that they've made an "agent connection." That maybe they have a chance to make it.
Always looking for that diamond in the rough so they can polish it to a brilliant shine, caring agents (yes, they're out there) work with new writers and first-time authors. That's a man or woman of great character. You may be lucky to be their big fish in their small pond someday. And as long as you're not a pain in the ass, caring agents will hold your hand through the entire process so both of you win big in the end.
And then ... some don't. They don't have to. They've got lots of little fishies in their big lake.
A writer wants a great agent, just like an agent wants a fantastic, best-selling writer. It's definitely a two-way street. If you're a writer, hopefully, you'll find an agent that "fits." But let it said, it's by far, the worst part about writing a book. Finding a caring, qualified agent. You'd like to think that if you do your job, act professional, and meet every deadline, (on top of stellar writing) that you're a diamond.
But in the end, writers are looking for those diamond agents, as well. Sometimes we just have to dig through a mountain of coal to find them.
Blessings to you and yours.