How do I proceed with a book idea?

People have often suggested I write children’s books, but there are already so many out there. I never really thought I would have a truly original and interesting idea.

Well, I suddenly have what I think is a very good idea for a set of children’s books. I know I need to put the idea in story form, but then what? How do I find an illustrator – especially without paying anything unless this endeavor turns out to be a success?

Do I need to have it illustrated before I submit it to publishers or can I just submit the story and let them worry about illustrations if they like it? I feel like having illustrations already done will make it look more complete and help express the whimsy of the story, but I really just don’t know.