I've been an audience member at a handful of panels/talks/signings at lit festivals. Any funny story related to writing/topic at hand will go over really well. Like, this funny thing happened to me while I was writing, or this person said a hilarious thing to me at a signing, or whatever. Staying cool under pressure is a must. and knowing your genre really deeply/being able to draw new connections within your genre for the audience. Having cool advice/tips for aspiring authors in your mind, ready to dispense, would probably serve you well. If there's any weird nitpicky stuff or tiny inconsistency about your book, and you have a hard-core fan of your work in the audience (you know, like Comic Book Guy from the Simpsons), you will be challenged on it, so have something smart to say. But audiences at panels generally think the authors are super awesome and smart and full of clever ideas, so you are already starting out on top!
Coolest author I saw at a book panel was Joe Hill. Not because of his work, which I've never read, but because of what happened at the panel. (Preface to the tale: Joe Hill's dad is Stephen King.) During the Q&A section of a SF/Horror panel, a weird old dude got up to the mike and said something like, "The horror genre is in a terrible state, and it has gone downhill since H.P. Lovecraft died. Modern horror is just dreadful, AND THE BLAME RESTS FIRMLY ON STEPHEN KING!" Everyone was silent. For a second I thought the panel was going to end in bloodshed.
Now that's incredibly rude, to him and his fellow horror writers and his dad, and technically not even a question. So Joe takes a deep breath, and launches into this incredibly passionate and eloquent response that totally broke the guy off without even insulting him. The line I remember was something to the effect of "I think that my father writes the experiences of middle-class america, and his work really connects with people." The audience erupted into applause after that, and the Stephen-King-hater slunk back to his seat. My partner and I came away from the panel thinking that Joe Hill was a really kind and classy and intelligent guy. We don't even read much horror, but we tell lots of people how we saw him talk and how smart and cool he is. So there you go.