Let's start out by reminding you that I am an author, not a publisher or agent. Consequently, "the business" is as much a mystery to me as it is to you. Listening to my advice makes as much sense as letting the guy valet parking your car tell you how to design a race-car engine.
There are 4 elements you will need to have success as an author:
4.More concern for your audience than for yourself.
The first two items on the list are negotiable, the second two are not.
The children’s book market is very difficult to break into. Publishers and agents receive vast boatloads of submissions every year. It is said that you have a greater chance of being cast in a network sit-com than getting published as a children’s author/illustrator.
For context: I tried to become published having written for children professionally for a decade, with 6 Emmys (for Sesame Street) and a few kids TV series under my belt. So, I had it relatively easy. It only took me 2 years to find a good agent and 2-1/2 years to get my first contract (for Don’t Let the Pigeon Drive the Bus!).
“Writing” involves a colossal amount of re-writing. “Illustrating” involves a colossal amount of re-drawing. While it can be thrilling to knock out a great first draft, I know no professional writers who do not spend many months revising over and over again before they dare show their work to their editors. From acceptance of a manuscript to publication can take anywhere from 18 months to 4 years.
Keep in mind that there are many books out there vying for Grandma’s dollars. For the vast majority of Children’s authors, it is not a lucrative career. If you are looking to make lots of money, I recommend getting into crime.
I know all this sounds grim; it is.
On the plus side, publishers need good books and hire editors to find them. If someone tells you that your type of book isn’t being made, say, “yet”. While an agent isn’t strictly necessary, I highly recommend acquiring one (do your research, make sure your prospective agent handles the types of books you write/draw).
To get started, find informative websites, such as the Children’s Book Council’s and The Society of Children’s Book Writers and Illustrators'. I’d also get as many publisher’s catalogs as you can to familiarize yourself with what they are publishing, who is writing and illustrating work you like, and who represents your favorite author/illustrators.
If I have advice it is to write as much as you can. Not just in a journal, but for an AUDIENCE. Write articles for your local paper, newsletters, blogs, etc. Create little books and send them to friends, clients, etc. This will help you find a voice and, maybe, get noticed. In addition, it is good to read up on current child development approaches (many education journals publish articles and studies) and attend a few seminars on how children learn.
You might also workshop your ideas with a bunch of kids. They can be found in most schools and I'm sure hip administrators wouldn't mind a library visit from a real artist.
Remember, your job is to think ABOUT your audience, not FOR your audience.
Please feel free to ignore any of this advice and good luck. I hope to see your work on the shelves in the near future.