If the wiring in the existing outlet ends there (doesn't go on to another outlet somewhere already), then you can send the wires out from it to the new one (no junction box). Black (hot) wires go on the brass colored screws, white (neutral) wires go on silver ones, ground to ground (obviously). So, if there's just the one set of silver/brass screws being used in the existing outlet, then hook the new wire onto the other set of screws (doesn't matter which set of wires uses top or bottom screws - as long as one set is on the top only, the the other is on the bottom only; no cris-crossing... hope that makes sense).
THis is real easy. I just did this this past weekend. Go to home depot or hardware store and get a "Blue Box" that says "OLD WORK" you get get a box for 2 outlets or 4 outlets. But remember, just because you are putting 4 outlets in doesnt mean that you can hook up more stuff. It is still running off the same main breaker. Take the box and put it up to the wall and draw a circle around the box. Take a drywall saw, works better then a box cutter, and cut where you drew the lines. Try to work the box in so that it fits. you might have to continue to cut the whole out, but take your time. You don't want it to big. Just enough so that it is snug. Now don't install the box yet.
Turn off your power to the outlet from your main breaker. Plug a light or a fan into this outlet so you know when you have turned off the right one. Once you are sure the power is off, unscrew the screw on top and bottom of the outlet so the outlet comes out. It will still be connected by the wires. Get a lenght of 14/2 wire from hardware store. This should be rated at 15 amps. Get a 15 amp socket/outlet also. It will say 15amps on the outlet, or 2 if you are going to use 2. Now you are going to use the outlet that you have end hook the other one the same way. You should have a black wire, white wire and green connected to the outlet. You need to put the new wire through the existing outlet box so that you can reach the new box. So now you should have a 14/2 wire going from the inside of the existing box, through the wall and into the new box. Rember, the new box should not be connected to the wall yet. You will see the back of the existing outlet and where the wires to. One, either black or white will be connected to the left or right of the outlet. you need to copy that on the new outlet.
Strip some of the protection back so all 3 wires with their insulation are showing. You should see screws on either side of the existing outlet. That is where you are going to connect the new wire. Take the black wire and strip about a 1/2 inch of insulation back. Now unscrew one of the screws that is on the side where the black wire connects to the existing outlet and connect your new wire to that side using those screws. There might be a push in area, but that is probably being used by the existing wires. Now strip the white wire and connect that to the side where the white wire is on existing outlets. Take the green wire and connect it to the Green screw on the existing outlet. That is the ground.
You should have the wire going through the back of the blue box that you are installing.
Now all you have to do is connect the wires to the new outlet.
Do that by looking on the old/existing outlet and taking the black wire and connecting to the same side of the new outlet. Same with the white wire and then connect the ground to the green screw.
Now pushe the blue box into the new whole. There should be a small screw on the top and the bottom of the new box. That is connected to taps that when screwed in will come up and attach your your dry wall. That is what holds it in place. It's easy to see and understand.
Now take the new outlet with wires attached and attach it to the blue box.
Now switch the breaker on and test the outlet to see if it works. It should. Cover it and you are all set. Good Luck.
