A first-time writer needs to have the ENTIRE novel done before approaching an agent or publisher. Print it in proper manuscript format. You can find guidelines in most how-to-write books.
First you have to find the right agents to send your book to. I used Jeff Herman's Guide to Book Publishers, Editors, and Literary Agents. Jeff had agencies fill out a Q&A which details what they like to represent and what they don't. Grab a pen and start circling those agencies that sound like they would want to represent your material (obviously you don't want to waste your money and their time if the agent only represents non-fiction and you have a fiction piece). Once you have a list, then follow proper submission guidelines. Include a ONE-page query note (consisting of a hook to the story you're writing, why you're the best one to tell this story, the proposed market for this story, and any publishing credits); the first 50 pages of your novel, double-spaced and free of errors; a brief synopsis (5-6 pages); and a SASE for their response.
Then start sending it out ... and sending it out!
Now, that all said, here's a warning: There are a lot of scam agencies out there. NEVER pay one cent up front for ANYTHING (not a reading fee, not a copying fee, not an editorial/book doctor fee). If you get such a response from an "agent," immediately toss it into the trash can, because that's where your money will be going if you fall for that ploy.
So that's the skinny on "the agent hunt." Be wily, be persistent, be patient ...
One of the worst things for unpublished authors is having their manuscripts returned to them with a rejection. That's a tough part about writing. Eventually you have to send your baby out into the big, mean world and hope it is not treated too poorly. But it always is. Rejections are a matter of doing business for a writer. Chances are, you will be rejected many times.
How I handled it was by never giving up. You need persistence. I would float out ten query letters to agents. Every time I got a rejection, I would simply send out another batch of letters. That represented another ten chances of getting published, with more chances waiting in the wings. This helped to take the sting out of those many, many, many rejections.
I get asked a lot about writer's groups or critique groups. There are different schools of thought on this. I'm on the pro-side of critique groups. I think they provide a valuable way to get feedback on your writing. In fact, I belong to a local writer's critique group. I started with this group when I was writing short fiction, and after about 20 published novels, I'm still with the same group. They are my proverbial "first readers." I value their opinion and input. Not a page gets published that is not read and commented upon by them first.
You may not be able to find a good critique group. Start your own. Or at the very least, identify a group of "first readers" that you respect and who will give you honest feedback. Although, yes, you do want to hear that a friend loved what you wrote, you also want to hear what parts of the story work and what parts don't, what characters are not believable, what actions are illogical, and what detail you overlooked that was obvious to someone not so close to the writing. Even after all these years, my critique group members surprise me with their observations, expertise, and generosity.
Becoming a published author basically boils down to a few key actions: Read, Write, Persist.
Read. Read everything in the genre in which you want to write, but don't limit yourself. Read broadly. The best teacher of writing is a good book.
Write Every Day. Even if it's only a few paragraphs, set aside some cracks in time to spoil yourself with the luxury of writing. If you write every day and read every day, your own skills will improve constantly. As you write and stumble on a scene or ponder some technique to develop character, you'll find the answer in the next book you pick up and read. You'll hear yourself constantly say, "Oh, that's how you do that!" So let me repeat: The best way to learn to write is simply to read.
Be Persistent. Once you're happy with your project, chuck that baby out and keep sending it out there until someone notices. Also allow the power of networking to help you: go to conventions, writing conferences, book signings. Talk to authors, agents, publishers. Sometimes this can be the back door into getting your own work noticed.
So there you have it: read every day, write every day, and persist in your dream.