Summarize:

The first step is to look up good publishers. Here is what to look for in a publisher:  Do they publish books you like? Do their published books often have mistakes? (Typos, missing pages/pages out of order, etc.) Do they publish books in your book's genre/age level? Will they publish your book if you don't have an agent? Are they well-known? Once you've found a few publishers you're absolutely certain you like, send in your novel to your top 30. Be prepared for rejection, a lot of publishers are picky about what they publish. Don't take rejection too hard, either. It's bound to happen at least once, even with the greatest novel. Acclaimed author JK Rowling received multiple rejections before her Harry Potter series was a success.  Don't be afraid to try many publishers at once; the first one to accept it gets it! If that doesn't work out, at least you wrote a novel!
Accept that publishing can be hard. Send the work in. Try self-publishing if the publishers don't come through for you.