Identify local vendors first. These vendors will be the easiest to solicit as they are typically small businesses located in your home town, you have a relationship with them and they often have kids in school, so they understand the funding issues.
Identify committee chairs who will focus on local vendors. You might have committees by area or by type of business. Often, the parent organization has a standing relationship with a vendor, so reaching out to that vendor will be easier.
Solicit local vendors in person. While the vendor may need a letter with the PTA or parent organization's tax ID for IRS filing purposes, most vendors respond better to an in-person solicitation than they do a form letter. Plus, it's much more difficult to turn down a school auction request from one of your best customers.
Identify national vendors. If you have a chain grocery store, drug store or clothing store in town, go to their website and see if they have a process in place for solicitation of donations. Many vendors have foundations defined specifically for this purpose, and you may find that your auction doesn't qualify for their funds. If this is the case, approach the local store manager. Typically, though you may not receive a substantial donation, you can at least receive a gift card as a donation.
Generate a form letter to send to national vendors. Write a letter with the school auction information, purpose of the funds and the parent organization or PTA tax ID. Send this letter on to national vendors that you believe might contribute. If you have a contact, use it. National vendors receive a multitude of these requests. So ask early, ask often and use whatever contacts you might have in your parent community.