Being auto-approved by a publisher means you are now instantly approved for any of that publisher (or imprint)'s titles on NetGalley. Just press the REQUEST button as you normally would, and you will receive an approval notification right away.
Take advantage of your auto-approval! Be sure to use the Auto-Approvals section under Browse in Find Titles and on your Dashboard and check back for new titles from that particular publisher on a regular basis, since you'll be able to access those titles as soon as you press REQUEST.
If you have a question about which publisher or imprint you're auto-approved for, contact support. NOTE: It is a good idea to save the original "you've been auto-approved" email notification, and forward that along to us with your inquiry.