Check that the power to the outlet you're working on is turned off. Go the to breaker box. If the outlet is in the bathroom, check that the switches labeled "bathroom" are turned to the "Off" position. Turn off all switches labeled as "bathroom" if there are more than one.
Test the outlet by plugging in a light to ensure the power is off. The light will not come on if the power is correctly turned off. Remove the top plate screws and plate, then unscrew the GFCI. Loosen the black wire screw and remove the wire, then remove the white wire. Finally, remove the ground wire, which usually looks copper. Throw the old GFCI outlet away.
Read the new terminal to identify the black, white and ground wire slots. Put the wires into the appropriate slot and tighten the screw.
Put the new GFCI back into the slot. Secure it in place with the screws and top plate. Turn on the circuit breaker.
Test the new GFCI. Press the "Reset" button and insert a light into the outlet. The light should be on. Press the red "Test" button. The "Reset" button should pop out and the light should go off. If this doesn't happen you wired the GFCI incorrectly. Press the "Reset" button once more to enable the outlet once again.