Become familiar with the reference books of the trade. Learn that research is the key to success. Here are some great sites to aid you in your research. Just remember that there is no substitute for reading and enjoying the children's books themselves. Unless you plan to self publish your story, there's really no need to look for an illustrator.
Most publishers prefer to work with their own stable of talent.
They would much rather pair up a proven illustrator with a first time writer to give a book name recognition. Editors also prefer to choose illustrators based on their style of artwork. They match up a particular style of art with what fits the mood of the story. First of all, recognize that publishing a book is a business. In order to succeed in any business you must be knowledgeable about that business and adopt their professional practices and procedures.