It would be very important to cover the mood / feeling of the person who's doing the facepalm, more than the description of the act itself.
With due respect, some of the descriptions of provided in the previous answers look like the person is actually hurting himself / herself.
So it's quite important to define the mood, the feelings, the frustration of the person doing the act first before actually defining it. This gives more weight to the person's reaction.
"After hearing the same question posed to him for the umpteenth time, a deep guttural sigh, conveying intense pain, escaped Bob's lips as he extended the palm of his right hand and covered his bent face with it, fingers tightly clasping the skin. It was a classic 'Why do I have to deal with these type of people?' pose."