Sorry but you cannot upgrade just the processor since it is soldered to the logic board. What you can do is to change the logic board to a faster one. I.ex. you have a A1278 late 2011 and all the logic boards share the same connectors and will fit.
Apple has named the unibody pro 13" for model A1278 through several upgrades. This means technically all boards from this model will fit. But they often change the speaker assembly or cable position for the iSight or bluetooth connector so you would have to mess with those parts too if you i.ex. try to install a 2009 logic board in a 2011 A1278.
If you got hold of a 2.8Ghz i7 logic board in the same production cycle (late 2011) it would fit. I did that several times. I got a 2010 2.4ghz i5 MBP A1286 and bought a used 2.66ghz i7 board that is running fine, everything fits fine.
This is from one of my friends at Apple.
"Is it possible to upgrade the processor? Probably. It'll be difficult though. Laptops are especially tricky. You may need a new logic board. Apple doesn't allow processor upgrades under warranty, so if you try and fail, Apple will do absolutely nothing to help."
From the schematics I've seen, the processor seems to be set into the motherboard and not made to be easily removed. So there is a danger in replacing it as you might damage the logic board on its removal.
So, final answer? It can be done.
Just not easily.
And it could prove to be a very expensive mistake if it isn't done right.