The process is quite simple and you can locate tons of help on
Google.
The basic process is as follows:
1) Download to your desktop the most current drivers for your new GPU from
AMD or
nVidia. Make sure and get the proper driver package for your operating system.
2) Uninstall your current video card drivers and turn off the system.
3) With the power off and the computer unplugged, carefully open the case and remove the current GPU.
3a) Since you have probably never cleaned in there, blow the system out with a can of compressed air.
4) Install the new GPU, close the case back up and plug everything back on.
5) Boot back to windows. When the Os loads, it will detect the new GPU. Cancel all of the windows prompts then run the installer for the driver package. Follow the prompts, restart and enjoy!
Be sure to keep in mind that you may need to install a new PSU depending on the GPU you get.
Anything over a 4670 (decent GPU) or a 9500GT (about half as fast for the same cost/power consumption) will need a quality 380-500w PSU, depending on the GPU.
If you have to upgrade it, get a quality Corsair, PCP&C, Seasonic or Antec Earthwatts PSU.