I wrote a children's book and I have read it to several people (not just family members) and based on feedback, I believe it is good enough to be published. It is completely original and I cannot find any similar books on the market. I really want to publish it to share my creation with the world. It's a story that is both educational and funny and I believe kids today would enjoy reading it. (If it helps the reading level of my book is about a third grade level).
Get a copy of "Children's Writer's and Illustrator's Market." It explains the whole process. Your library probably has it, or you can get it from any bookseller.
Do your research -- books for 3rd graders have a specific name given to them (they're not picture books, which are limited to 500 words or less), they're called Chapter Books.
Not only do you need to be very concise with your wording in them, you have to have a theme and a 'message'. And you need to find an agent who deals with that age group as well as fiction.
The kids book market is immensely hard to get into, everyone thinks it's easy doing a kid's book but the amount of titles bought each year by publishers of children's books is a fraction of the general fiction market. Only the best make it through.
The easiest way to publish a book without being rejected is self publishing on Amazon. That being said, it won't get as much exposure as it would if say, you approached scholastic and by some miracle, they published it.