The first step in any electrical project is to make sure the main disconnect on the service entrance panel is at the "off" position, or pull the main fuses out. As an added safety measure it's a good idea to tape note on the panel to tell others what you're doing so no one will replace the fuse or reset the breaker while you're working.
The next step is to test the outlet with a light before handling any wires related to that outlet. Once you've determined that no electricity is flowing through the area - you can go ahead and work in safety. Now it's time to begin work on the outlet. Unscrew and remove the cover plate then unscrew the outlet from the junction box. Pull the outlet out from the box and and unscrew the ground wire - the one with green insulation - first. Then you can unscrew the other wires from the back of the old outlet. Using wire cutters, clip the wires at the insulation, then, using wire strippers, strip 3/4 of an inch of the insulation from each wire.
Next you want to attach the wires to the new outlet. The black wire should be connected to the brass screw and the white wire should be connected to the silver screw. To properly attach the wires - hook them clockwise around the screws then tighten the screws with a screw driver. Then re-connect the ground wire. Once all the screws are in place, put the outlet back into the box and replace the screws. Then reattach the wall plate.
It's now safe to restore power to that outlet and test to make sure the new outlet is working properly.
As I stated before, it's important that you need to be safe when working with electricity. The human body - just like metal wires - is a conductor of electricity and the possibility of getting a shock increases when any part of the body gets between the electric current and the ground.