Wiring for a ground fault circuit interrupter (GFCI) depends on where it falls in the circuit and whether you want it to protect the other outlets.
Turn off the power and look into the box to see whether the receptacle is at the start, end, or in the middle of a run. If it is in the middle or at the start, it can protect other outlets. Consider any drawbacks to protecting outlets in the circuit after the GFCI. Do you risk cutting off power to a freezer if the GFCI trips, for instance?
About 25 minutes to remove a receptacle and install a GFCI
Screwdriver, side cutters, strippers, lineman's pliers, voltage detector
Stripping and splicing wire
Lay a towel or small drop cloth on the surface below the receptacle.
GFCI receptacle, wire nuts, electrician's tape
If you want the GFCI to protect itself and the outlets downstream, find out which wires supply power (the line wires). Cap all the wires with wire nuts except one black one and turn the power back on. Place a meter across the black wire and the ground wire or metal box. If there's no reading, it's a wire in the load cable; if it reads approximately 120 volts, it's a wire in the line cable. Double-check by repeating the test with the other black wire, turning the power off to move the wire nut and on to test the wire.