There are lots of articles offering authors advice on their author photo, which seem unanimous mainly about hiring an actual photographer. The best of the bunch was Porter Anderson's "Facing Up to the Importance of Your Author Photo." Some of Porter's advice:
The best background is no background. Friends won’t let you drive drunk, and professional photographers won’t let the Eiffel Tower emerge from your left ear.
Don’t hold your book(s) in your shot. Nothing says carnival barker like an author clutching his or her book(s) in a photo. Remember: dignity is a virtue.
It’s a headshot. Not an upper torso shot. Not an arm-on-the-back-of-the-sofa shot. Not a you-and-your-kids shot. Your photo has to convey accessible, intelligent personality in the tiny space of a Twitter thumbnail. “Headshot” means your head. We want your face up-close, not your furniture.
Arguably, his best tip was:
But the true secret to a great photo is always having something on your mind at the time the picture is taken. It’s so easy to go mentally blank as soon as the photographer says, “Ready?” So be ready with an idea, an image, a voice, a person, even your grocery list. Just put your mind to work on something and your personality will surface nicely.
Check out the full article here.