I've completed my first novel and done as much editing as I think I can as the author. What should I do next in order to get this out there?
Typically, you would begin querying agents. Agents offer a number of benefits:
The cost of an agent is a commission on your work, if it sells (and not before!). Usually this amounts to 15%.
EDIT: As MGOwen points out, there are some incompetent and/or exploitative people in the agenting business too. Preditors and Editors is an award-winning website that can help you check up on agents to make sure they're on the up-and-up. You should also look for agents that are members of AAR - the Association of Author's Representatives. This is the primary professional organization for literary agents.
Querying an agent usually involves sending a query letter and the first few (rarely more than 5) pages as a sample. Agents will specify the exact format they desire, and they will almost all be slightly different. Writers Market is one of the better-known resources for agent listings. Note that they are a paid service. (They also have print editions). For the most part, agencies are all on the web these days, and they should describe their preferred formats on their site.
A great resource for learning about how to craft effective query letters is Query Shark. Miss Snark's Blog also says quite a bit on the subject (though that blog is no longer updated). I'm sure there are other good resources out there too, if you do a little searching.
If your query piques the interest of the agent, they will usually request a "partial" - basically a larger chunk of your manuscript, like 30 to 50 pages. Then, if they still like what they're seeing, they'll request the whole thing.
Finally, if the agent likes the entire work, they will offer representation. Alternately, they may ask to see a rewrite before offering representation. There are a number of things to consider at this stage, namely how well you and the agent "fit". Numerous agents offer advice about this on their blogs, but I won't go into detail here.
Once you've signed a contract with the agent and gone through any revision, they'll begin shopping your book around. Hopefully everyone loves it, there's a huge multi-house auction, and you can retire!
While querying agents is the most well-known way to get a book into print, there are alternatives you can explore.
Some publishers will accept queries or full manuscripts. You may choose to submit directly to these publishers. Small presses may be more likely to look at your unrepresented work. If your book does garner interest, you may choose to deal with contract negotiations and the rest of the business side of publishing on your own. A better alternative is probably to get an agent at this point. It won't be hard when you tell them you already have a publisher who wants to buy your book.
Another option, "Vanity"/self-publishing, is more popular than ever. Be extremely wary, however! "Vanity" publishers will disguise themselves as small presses, large presses, and anything else they think will get you to fork over your hard-earned cash. In traditional publishing, the money always flows toward the author. If you see anything about up-front fees, you're typically looking at a vanity publisher. Most of these businesses make their money from authors, who pay significant sums to have their books published.
If your main concern is seeing your book in bound form, and you don't mind paying for it, this path may be for you. Just be aware of what you're getting into. Vanity presses make their money from authors, so they have little incentive to actually sell books. They offer no marketing support, and your book will not generally be stocked on bookstore shelves or get reviews. Most books published through these companies sell only a handful of copies. It is possible to sell large quantities through self-publishing, but it generally requires a lot of hard work on the author's part, promoting and marketing. A platform, such as speaking engagements, can also help. Even then, it's a bit of a long-shot.
Finally, print-on-demand is an emerging alternative which allows books to be printed one-by-one, rather than in large runs. Companies that offer this service typically take a cut of each book sold, and are able to remain profitable by keeping minimal inventory.
Publishing through print-on-demand shares some of the pitfalls of "vanity" press, namely the lack of any support from the publisher. Print-on-demand is probably even less likely to assist with formatting the manuscript for publication. However, the cost of entry is generally much lower in print-on-demand.
Do Your Homework
This post has already gotten rather long, and it's nowhere near being exhaustive. Publishing is a complicated business, and it pays to do your research. Find some author, agent and editor blogs that talk about the business. There are literally hundreds of them these days. Read up. Ask questions when knowledgeable people are willing to answer. You can never be too prepared!
My advice would be to write your second novel, and then maybe even a third, before doing anything else. You'll learn SO MUCH from writing two or three, that it will help you to go back and make your first one even better (or, if you're like me, recognize it for the heap of rotting garbage that it is and toss it). As far as I know, it is incredibly rare for someone to sell their first novel. And I've read on more than once occasion that this is a good thing. Writers grow as they write, and it's not always good for readers to see us in our very early, learning stage.
I'm not saying you shouldn't try and market it, mind you! I hope you can; I hope it's good enough and does great and we all get to enjoy it someday. :-) But you might very seriously consider writing a bit more before you do anything else with it just yet.
In the days of the Internet, where anyone can publish anything he wants (mostly), you can also consider building up your own community of readers.
Yes, it is hard work (as everything else) and I do not even want to recommend it. But it is a possibility and you should consider it. A big advantage wold be, that you knew your readers. You do not do that when getting published the traditional way. You will get some fan mails, but are these representative?
Seth Godin is blogging about digital publishing and community all the time. So he is not publishing fictional books, which is a considerable difference. I prefer a book in my hands when reading fiction. But you also can publish them digital and on paper yourself.
Read these two blog entries to get an idea:
First Get some close friends, preferably a variety of types of people, to read it and give you feedback. There's nothing like other perspectives. I've also been a fan of Stephen King's advice to let it sit a bit and then go back and read it.
Publishing I'd suggest a multi-prong approach. J.A. Konrath has some interesting advice on his blog. I might hold back my ebook rights and self-publish on Kindle/Nook and see if you can get some sales. You never know if that might help you get a deal.
The post on Agents is excellent, and I'd read that a few times. It's probably worth trying to see if there is any interest from agents and if there is a possibility of sales.
Blog I've seen a number of writers use a blog to talk about their book, their craft, discuss their motivations, etc. in the non-fiction world. If you can write something interesting that keeps readers engaged, even teasers from the book, you can build some grass roots interest. This likely isn't going to get you profitable, but it might help you generate some sales, and perhaps more motivation to keep writing.
It's hard to judge your own work. If you think it's ready, but you're not sure, then you need to get more outside opinions. One approach is to try to find an agent. If a reputable agent takes it on, then it probably is ready. But that approach is relatively slow. And if you don't get any agent interest, that doesn't mean it's not ready.
Other ways to figure out if it really is ready:
Once you're sure it's ready, the other answers here have good information on querying agents.
In the last several months since this question was posted, e-books have surpassed hardback books in total sales volume. Two months later, they surpassed paperbacks in total sales volume. Right now there are more e-books beings sold than ever before, and you really need to look hard at giving this a try. Yes, there is more work involved, but the benefits are numerous. There is a whole new industry starting up, and you can find graphic artists who will design your book cover professionally for less than a hundred dollars. You can find tech gurus who will format your book and create the e-book files for less than $50. There is no actual cost for publishing and distributing the e-book, so it's esier than ever.
If you want a print version, the Print On Demand arena has become so much easier and more convenient. With sites like CreateSpace around, you can publish a print version of your e-book for no cost as well.
A couple of the biggest advantages are royalties and speed of entry into the marketplace. For a traditionally published book, you'll be lucky to get 17% royalties, while e-books offer 70%. With a traditionally published book, the soonest you will hold one in your hands will be 12-18 months. With e-books you can have a book published and cataloged for sale in two days, and a POD book can be in your hand and ready to be sold in a week.