The important thing to remember about many people who approach an author at a book signing is they want to feel special.
That means you should make an effort to look each person in the eye, ask them their name and how to spell it before you sign the book, and really listen to them [at least for a few minutes] even if they try to tell you the story of why they've always wanted to write a book themselves. Each individual who buys a book will, if made to feel special, tell a half-dozen friends how wonderful you are, generating more sales.
I have personally signed thousands of copies of my books and I've made it a practice to write something more than just my signature each and every time.
- If the person was quiet and shy and I was unable to determine where they're from or any angle to hang a phrase on, I’d write: "I hope you enjoy Veronica Slate [my protagonist] as much as I do. Thanks for buying my book."
- "It was great meeting you at [insert location here]. Hope you enjoy my book." [This one is especially good because it proves to others that they really met you. I know this may seem silly to you, but they really care.]
- If I discovered that the person was from Chicago, I'd write: "To my friend from Chicago. Cuddle up with this book on those cold, winter nights."
- If the person says it's a gift for, let's say, Aunt Grace, I'd also ask the name of the person buying the book and I would write: "For Grace. Tommy thinks you'll enjoy my book. I hope you do."
- If the person says anything, no matter how vague, about being a writer themselves or wanting to write, I would write: "To a fellow scribe. Good luck with your writing career." [That makes them feel special and included in your esoteric profession.]
If you are mobbed by lots of people, make a real effort to look each individual in the eyes as you accept the book for signing and as you hand it back to them.
Most of all, relax and enjoy it. People love to meet writers and love to hear us talk about how we write. Forget any idea you may have you’re nothing special, just a writer. I have spoken at libraries, conventions and seminars. People are endlessly fascinated by writers like you and me. To a reader meeting you, you are very special indeed. If you make them feel special too, you have a fan for life. Don't laugh. More than a thousand people from all over America and several foreign countries have written me about my novels. Why?
Because I encouraged them to do so by listing my email address in the backs of my books. I've answered every single letter and won fans for life. They tell their friends and sell even more books.