I'd probably break into a pharmacy and spend the last day of my life twitching away.

 

Like others have said, I would probably refuse to believe I could be the last person on Earth. I mean...even if there was a ridiculously virulent plague, if I survived, someone else probably did, too. Even if it was a "rapture" type situation, and I saw the population of an entire football stadium vanish before my eyes, I wouldn't be able to believe I was the only one in the world.
I'd of course be studying survival skills and no doubt teaching myself quite a few things about mechanics, but I'd be searching the US, first in populated areas and then through the boondocks, setting up broadcasting stations, and perhaps eventually finding a way to travel to other countries in search of people. If I found no one, eventually I'd probably die, because surviving on your own is damn hard work, and takes luck just as much as skill.