How does an author set up a book signing?
Generally, the author doesn't set up the signing, the publisher does. As an author, you tell your publisher which stores you're willing to travel to and if you're traveling, the areas you're willing to stop to do signings in. Then the publisher contacts the bookstores and tries to set something up. Some stores love author signings, others refuse to do them.
If, however, you have a relationship with a particular bookstore—know the manager, employees, or buy enough books that they know who you are and greet you by name when you walk in the door—then just ask them if they'd be willing to do a signing and what they need from the publisher (usually free returns, posters, etc.) and from you (varies). Then let your publisher call them and work out the details.
And before anyone says, "I'm willing to do whatever it takes, but my publisher just won't work with me on the book signings," read this and this and this.