I've been getting this question a lot lately and I totally understand. It can seem overwhelming to find your way into a huge industry like publishing. Lucky for us, there is more information out there on publishing than ever. I'm going to do a series of posts answering this question and I'm going to start with something basic--revising.
You may have a great story, but it will get even better with revision. Put it away for a little while until you can get a fresh perspective. I find three months to be helpful. It's okay, you can work on writing something else while you're waiting! You could also go read a bunch of books in the genre you're writing. What? You're doing that already? Good. It's always fun, and when you read tons in your genre it can help you see what works in a story and what doesn't.
When you're ready pull that story out and revise it again (I know I'm ready when I can't stop thinking about the story!), as many times as it takes. Put it away again for a little while if you need to, but when you feel like you can't see anything else that needs to be changed you're ready for the next step, getting critiqued. There are many ways to do this, but the best method I've found is to trade with other writers in the same genre, or at least those that understand the genre. (I know, picture books are kind of a specialty, so I find this point especially important for what I write.) There are lots of ways to find critique partners if you don't have any: writer's chatrooms, local and national organizations, the library...I found my critique group on Verla Kay's Blue Board.
Once you've gotten your critiques, revise accordingly. I know, this can be difficult and the critique/revision process can happen more than once, but it's good to have an open mind and not take offense to anything anyone says. You are all there to help each other. (Yes I know there can be the occasional 'bad critique partner' but I think they are the exception to the rule.) Just keep in mind that it's your story. You don't have to use all of the suggestions. I do take all comments into consideration, and really take notice if more than one person points out a particular spot.
When your critiques and revisions are all done and you cannot see how in the world you can make the story any better it is time to a.) go to a conference and/or workshop and get a professional opinion from an agent or editor. No, this is not a requirement, but it can be pretty eye opening to hear what a professional in the business has to say about a manuscript. OR b.) start querying, which involves writing a query letter(and a synopsis for those of you who write longer books), studying the market(if you haven't already), and submitting to agents and/or editors. I'll do some posts on those topics soon.
Write on people!
Go to: I Wrote a Book, Now What? post #2 -- Market Research