…is the most popular question I get asked.
Typically, and author will submit a manuscript to a publisher, while an illustrator submits a portfolio of past work for consideration.
An author need not have his mss. illustrated to submit; in fact, conventional wisdom is that it is unprofessional to do so unless the author and illustrator are one and the same.
My best advice is this book:
It is a great overview of the market, and really gives a sense of what they are in for, I mean, a list of all the wonderful possibilities!
In previous editions, there has also been a nice section devoted to opportunities for children to publish their work.
Happy writing!