I'd never give up thinking that there must be someone else around, so I'd build a shelter, I'd find a supply of food, and presuming that I still had books etc, I'd use those to keep sane, I'd sing to myself, I'd write notes to everyone just in case, then I'd just keep going out and about to find someone!
I'm not sure how well I'd cope - the devastation of mind is unimaginable - it would just have to be a challenge of pitting your wits to keep alive. It also depends on whether you believe you have a god with you.
You've almost got me panicking now! The more I think about it, the more I think I would have to hold on to the idea that someone else MUST be out there! Excellent question.