You say the last person on Earth, So I'm guessing you mean that there would be animals too. That would be cool to have them as company, as I would probably go insane if I was the only living thing on the planet. Still, I would feel lonely as the company of animals is just not the same as fellow humans.
But I would probably start with ridiculous small stuff near "home base", such as spray painting things (Such as smiley faces to keep me smiling, lol) on everything. And if everyone disappeared with no warning, you can bet I wouldn't wander far for a while, as how could I know what's going on out there? There could have been aliens or something that took everyone away. :S
But yeah, I would really hope I could get a generator going or somehow work a whole powerplant by myself (maybe hire a team of apes......), as it would be fun to access whatever I want. (Government secrets anyone?) :P
Once I was sure there was nobody else around, I would search through people's houses for anything useful/interesting, then pack it all up in someone's truck, and hope I could figure out how to drive it. :S
If not, then I would just travel by foot from big store to store, gathering whatever food could be cooked by fire, or whatever food I could just eat cold without worry of it rotting for a long time. I could just settle in one area until I ran out of food, but what fun would that be? I could probably bring a few or one of my cats as a companion, as it would be sad leaving them behind. At least every store would probably have some kind of food they could survive on, or they could hunt for something.
I would also probably make myself some kind of crown, and declare myself emperor of the world, as nobody could object. :P
And if I ever decided to settle down in one place for a long time, I guess it would be a good idea to gather seeds of vegetables from different stores, as I could grow stuff around one area.
You know, even though humans have made a big negative impact on the food chains of animals, it has come to the point that a lot of them rely on us for food. So if all the humans except for one disappeared, a lot of animals would probably be hopeless. :(
But yeah, I think I'm going on way too much, so I'll stop now. :D