So again, the first step to rewiring an outlet is turning off the power to the outlet. Even if the lights in the room go out, plug something in to make sure the specific outlet you want to work on is off. I found that plugging in a vacuum cleaner in the 'on' position was awfully convenient. So when I hit a breaker, I knew that outlet was off when the vacuum cleaner stopped. Saved me a lot of running up and down the stairs. (As an aside, labeling your circuit breakers carefully is time well spent)
After turning off the power, and double checking that the power is off, unscrew the cover and the outlet itself. Pull the outlet out of the wall with the wires still connected.
Replace the wires onto the new outlet in the same position.
Screw the new outlet into the wall. Screw on a new outlet cover. Step back and admire your handy work!
The process is the exact same for a light switch:
Unscrew the old cover
Unscrew the light switch from the wall
Make note of where the wires go
Unscrew the wires and replace them in the same positions on the new light switch
Screw the new light switch into the wall
and replace the new cover.
There you go! A quick and easy update for old worn looking outlets and switches. My last hurrah for the old house!