Set up a regular mailing campaign and mail color copies, postcards or printed samples of your very best illustrations to publishers or companies that you would like to work for. Do your market research first! If you buy a page in a sourcebook you will receive tear sheets that you can use as samples. Some sourcebooks are Picture Book , Directory of Illustration, and BlackBook.
DO NOT send slides or original artwork. Make sure every sample has your name, address, phone number, email address and website address on it. You might also enclose a cover letter, a response card (stamped and addressed) and/or SASE (Self addressed stamped envelope). Make sure your contact information is up to date and that you have the contact's name spelled correctly.
You don't need a formal resume but a list of previous clients in a related field would be a good addition, as is a business card. Keep track of what you have sent out, and what response you have gotten. Even with a SASE there will be many companies that you will never hear back from.
In some fields you can attend conventions or conferences that allow you to show your work to publishers or editors, usually by appointment. While you don't need to wear a three piece suit and tie, you should still consider what you are going to wear - at the very least be neat and clean. Be punctual about your appointments and remember your manners. (Do I sound like your mother? I hope so!)
SCBWI (Society for Children's Book Writers and Illustrators) hosts national and regional conferences that are a good opportunity to meet editors and publishers. GenCon and DragonCon are two of the biggest fantasy and gaming conventions where you can show your portfolio, meet with art directors and network with other illustrators.