Here's one, and probably the best, way to do this:
First things first:
Buy yourself a program called
Xpadder.
Wired Xbox 360 Controller:
Plug it into your PC's USB port and run the Controller through Xpadder.
Wireless Xbox 360 Controller:
You need to buy
this and plug it into your USB port, after that, you need to run the Controller through Xpadder.
...or if you want some other Controller, then just make sure Windows supports it and you can basically run it through Xpadder.
Now you might ask: "What Xpadder exactly does?"
In a nutshell: It simulates your keyboard and/or mouse, so that you can do basically all the same things with your controller than you can do with your keyboard and mouse (playing games, using web browser, using text programs, everything you can do on Windows).
It costs you few bucks, but I can assure you: It's worth the money!
I use Wireless Xbox 360 Controller on my PC with Xpadder and everything works perfectly.
BUT, I didn't get Penumbra: Overture to work well with it (swinging hammer/pick-axe didn't work that well).
...but other users here on the forums said that they got Penumbra to work without any problems with Xpadder.
My problem might mostly be that I didn't knew how to setup Xpadder correctly when I tried Penumbra with it.