DO NOT send slides or original artwork. Make sure every sample and communication 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. Mail a sample to yourself to make sure it survives the mailing process.
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. Email submissions may not get a direct response either.
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. Practice a firm handshake - it really does make a good impression. Don't worry if you are nervous about showing your portfolio - let your work speak for itself and use the process as a learning tool.
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. Spectrum is a annual published exhibit of juried fantasy art and they have an annual convention Spectrum Fantastic Art Live.
There are some illustration directories where you can advertise your work:Childrens Illustrators, Picture-Book, Worklife, Folioplanet, The Ispot, Workbook, 3x3 Illustration Directory, The Directory of Illustration and its sister sites: The Medical Illustration Sourcebook, andPlay (Illustration and Design for Toys and Interactive Games). Contact illustrators who are using the directory you are interested in to see if they have gotten work from the site. If the directory publishes a print version you may be able to get copies of your printed page to use as samples.
Always carry business cards with you. You never know when an opportunity will come along.