A quick glossary of terms:
Xinput - Xbox 360 controllers are the only ones that support this natively. Most games are coded to use this for gamepads, meaning if you don't emulate this or have an Xbox 360 controller, you won't be able to use a gamepad with most games. (It can be emulated. See MotioninJoy and x360ce entries)
Directinput - All other controllers use this. Games won't work out of the box with these controllers.
MotioninJoy - Software that works as a driver/emulator for a PS3 controller with windows. Lets your P3 controller do Directinput, Xinput, or keystroke emulation.
x360ce - Converts directinput to Xinput through the use of profile setups.
xpadder - Converts diretinput into keystrokes, letting you use controllers on games that don't support xinput or directinput (such as minecraft).
Do you have an Xbox or PS3?
[I have an Xbox] If your controller is wired, plug it in and it should work. If it's wireless, you're going to need an Xbox controller wireless receiver. They're $20+ I believe. I think Amazon & Newegg sells them. This requires the least software tinkering with most games. Minecraft, etc. will still need xpadder.
[I have a PS3] Download MotioninJoy and hook up your PS3 controller with a mini-USB charging cable. If you have bluetooth support (or buy it) you can probably go wireless, otherwise the USB cable will work. See the glossary to better understand the awesome features of MotioninJoy. This is pretty easy to setup, as motioninjoy is all you need (no x360ce or xpadder).
[I have neither] PS3 and Xbox controllers are expensive. If you don't want to shell out for either, there are programs that can make third party controllers work with PC games. Power A Pro EX controllers from Toys R Us, for example, are very good. This will require a high degree of tinkering, as you're going to need the right driver and then x360ce and possibly xpadder on top of this.
My advice? Grab a PS3 controller and use it if you have one (least hassle, motioninjoy is easy). Use the Xbox 360 second (I hate xpadder setup). Get a third party if you don't own either, and be prepared to learn x360ce and xpadder. Xbox 360 and PS3 controllers too expensive compared to the $15-20 Power A Pro Ex.