Depends on what your goals are.
No matter what have someone who is NOT your friend but who is knowledgeable about the market to read your book. Edit and adjust.
Then decide if you want the book just published or do you want the book published by a traditional publisher?
Traditional publishing... not that many literary agents rep children's books if you mean picture books. There are a few. YA is a different story.
You'll need to write a query letter. Then research publishers who rep the kind of books you write.
Then research them. Make sure they are A) accepting queries and B) you understand what they want in their query. Do NOT call if they prefer an email submission.
Understand that many children's book publishers have their own artists and may not use your artwork even if they use your book.
They may also change the title.
Your query letter is your hook. You need to polish it until it shines. Also understand that some publishers will accept queries without an agent.
Most queries get rejected. So you don't burn your bridges, I suggest querying in batches of five. This way if you find that something really doesn't work or that your query is ineffective, you can adjust it before you saturate the market.
If you send your query to everyone and it stinks (even if the book is good), you've just burned your bridges on that book.
If you just want to publish, you can use CreateSpace, Lulu or Smashwords to publish your own book with ISBN adn artwork. Please sign up for Kindle usage as well.