Vahlee's got it. There is no definite answer.
Even getting picked up by an agent can take a long time, for starters. The general process is:
--You query them, they get back to you when they read the query. It could be days, weeks, or months.
--If they like the query, they might request a partial of the manuscript. They'll read it when they get a chance. It could be days, weeks, or months.
--If they like the partial, they might request the full manuscript. They'll read it when they get a chance. It could be days, weeks, or months.
Once you find an agent who likes the full manuscript enough to offer you representation, it's entirely possible that it's not going straight to editors. The agent might have some suggestions for revisions you might want to do to make the book more saleable. The time that takes will depend on you, and how long it takes you to make changes (or not, if you choose not to.)
Once the agent does start shopping it around, there's really no telling how long it will take to sell. Maybe what you have is a subject that's hot right now and it'll get scooped up quickly. But the problem with "hot right now" is, it might not be hot in two years, which is about how long it'd take for your book to be published. So maybe tween vampire romances are the big thing today, but editors are taking a longer view. They might feel that the genre's glutted with them and pass.
But just like the agents, editors are also reading and working on several books at any given time. We're back to "it could take days, weeks, or months" before an editor reads it. Then, if they do want to buy it, they usually have to bring it before the other editors and decision-makers at their publisher. They have to show their plan for the book: how much they can pay for it, how much they think the book will bring in (which ideally should be more than what they pay for it). If they get the go-ahead to buy the book, then you have yourself a sale.
But wait! Contract stuff! Your agent's going to want to take a look at that, and maybe there's some room for negotiation there. I don't know how long that kind of thing takes. Probably not terribly long, compared to the rest, but it might also depend on what changes you and your agent ask for.
Okay, so, NOW you've finally sold a book. Contract in hand, woo-hoo!
Except, you're not done working. Charlie Stross has an excellent post on the process here. Very much worth the read.
So, even if it gets snapped up by an agent overnight, you're looking at a minimum of two years before it hits shelves, but the reality of it is, it's probably going to be longer than that.
Well, I guess you left me with some feathers in my hand.