Adding an electrical outlet is easy and can be performed safely if you follow some basic precautions.
First you need to determine where the new outlet will be. You need to also determine where you are going to get the electricity from. Usually you want to run the wire from the nearest electrical outlet. You also need to mount the electrical box to the wall. This can easily be done by using a retrofit electrical box. A retrofit electrical box has tabs that lock down the box to the wall. Just trace the outline of the box onto the wall and carefully remove the sheetrock with a utility knife.
Next measure how much wire you will need to go from the existing outlet to the new outlet. Be sure to take into account the horizontal run and vertical run when measuring. Once you have the length of wire, increase it a couple of feet. So if you measured 10 feet of wire needed, cut 14 feet. It is also important to use the correct wire gauge. Most United States homes use 14 gauge wire for AC electrical service. This wire is often called Romex and actually has 3 wires inside an insulated sleeve (Black wire (hot), White wire (neutral) and Ground wire (copper)).
Once you have your wire cut, turn off the electricity to the circuit. This can be done at the circuit breaker box. Once the power is off, use a receptacle tester to verify that no power is running to the receptacle that you want to run the power from.
Next run the wire from the old outlet to the new outlet. You may need to drill holes into existing studs to feed the wire through. If you need to span more than one stud, you may want to remove a piece of wall board or sheetrock. This will allow you to see any obstacles between the existing electrical receptacle and the new one.
Now it is time to start wiring. Connect the wire you ran to the existing receptacle. The black wire goes to the brass screws, the white to the silver screws. The ground goes to the green ground screw.
Now repeat on the new outlet, black to brass, white to silver, and copper to green. If you are using a retrofit box, the tabs in the back of the box will securely hold the wire in place.
Secure the new receptacle and cover and existing outlet receptacle cover. Restore the power and test both receptacles using an electrical tester. If you have removed any wall board, replace, spackle and paint.