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Turn off the breakers and the electricity to the room. To be extra safe, use a circuit/inductance tester to make sure there is no power running through the wires.
Remove the socket plate and outlet and inspect the wires. Test the outlet again to be sure there is no power at all. If the fire damage has melted the protective plastic sheathing, you should hire a professional, rewiring is a job for the pros.
If the wiring is salvageable, unscrew the wires and remove the damaged outlet receptacle. Remove the wires in the following order: Start with the black (hot) wire, loosen the screw that holds it by turning it counterclockwise. Then do the same to remove the white (neutral) wire then lastly, the ground wire. Using a wire cutter/stripper, snip off about a 1/2” from the end of the wires and strip off an inch or so of the protective plastic coating.
A ground fault circuit interrupter (GFCI) reduces the risk of a serious or lethal shock and electrical fires. They are mandatory building code in all kitchens, bathrooms and outdoor areas. GFCI outlets continuously monitor the electrical current traveling through the circuit and will immediately cut power to the receptacle if it detects any change.
GFCI receptacles are stab-back receptacles. Rather than wrapping the exposed wire around the corresponding screws, the wires are inserted (stabbed) into the designated hole at the back of the receptacle then secured with the adjacent screw. The black wire, or hot/live line, gets inserted into the hole with the brass screw. The white wire, or neutral line, gets inserted into the hole with the silver screw. And the green wire, or ground line, gets inserted into the hole with the green screw. Electricians have a saying to help differentiate the different colored wires: “Black to brass and green to ground.”
Wrap the exposed metal of the receptacle with electrical tape. Wrapping the metal prevents sparking if the receptacle needs to be removed again for repair. Also, if a foreign metal object were to hit the exposed metal while the receptacle was live, there is a chance it can arch and throw sparks. Gently push the wires back into the box, then line up the mounting screws with the corresponding holes and tighten. Be sure to install the receptacle with the neutral side up. If anything were to fall onto the receptacle, it would hit the neutral and ground wires first and eliminate any chance of an arch. The half-round slot at the front of the receptacle is the ground slot and the larger slot above the half-round is the neutral. These should be installed at the highest point of the wall. Cover the outlet with a plastic plate. Turn the power back on at the circuit box. Test the outlet by pushing the test button in the middle of the receptacle. If the reset button pops out it means the outlet is live.
If you have any questions or fears about working with electricity, call a licensed electrician. This type of work can be very dangerous, and there's no use risking your life just to save a little money.