Dear Troubled in Texas…
Assuming your art can compete with that being published in the current market, I recommend you try to get a literary agent who represents children’s book illustrators. She’ll constantly pitch you to editors, she’ll know about manuscripts already under contract with publishers but needing artists, and she’ll help shape your career. Do submit directly to editors and art directors, too, via postcard mailings; those folks will keep the cards on file if they like the art, but you must send new cards to stay on their radars. Also make a portfolio that shows off your style, characters, color palette, conceptual thinking, and design sense to show that you understand the opportunities of the picture book format, like page turns and perspective shifts. To learn that, study picture books in stores or take a picture book illustration course. Above all, join the Society of Children’s Books Writers & Illustrators. Its resources include how-to’s and directories of agents, editors, and courses. Your local chapter periodically hosts agents, editors, art directors, and experienced illustrators for portfolio consults, and you’ll learn the pub biz itself, not just how to break in.