Actually, I just finished putting in a supplemental outlet - saw this thread, so I figured I would take some pictures to show the process.
-->Disclaimer: I'm not an electrician, do not attempt if , etc...
Gather up your tools - You'll need things like this:

In my case, I needed another outlet inside the equipment room that was on the same line/circuit as my riser plugs and step lights (X10 to IR transmission cure). Got to get rid of the electrical plug that's pictured in the riser above.
Shut off the breaker to the circuit, and confirm that it is not live. Confirm it twice or more if you're paranoid like me!
Remove the old receptacle to expose the wiring - look around with a flashlight to see which side is mounted to a stud. this may give you some idea of any obstructions between you and the new plug location. Maybe run a stud finder along the path, and see if there's anything there (knocking and listening for density changes works to a degree also).
Grab yourself an EasyBox:

These are designed to go into a cutout, and have the top and bottom plates screw tighten against the drywall from behind. Really nice design!
Find your credit card! No, not for the electrician, but I learned it jut so happens that it is the same size as the hole you want to cut. I've found many ways to use a credit card for my build


Measure off where you want the new outlet, bearing in mind any potential obstacles that may sit between the new and the one you're tapping off of (fireblocks, plumbing stacks, dead mice, inlaws....). Trace your card...

You are under no obligation to use your kids' Halloween pencil, but you can if you like

. Grab your drywall saw (couple bucks at the hardware store) and do your best to stay between the lines

Fish tape or equivalent - you'll need something to get the wire from the old box to the new. If there's no insulation or obstacles, you may luck out and be able to push/pull the raw wire through....you'll have to determine which works in your situation. I lucked out, as I wanted my outlet on the back of the wall from one of my steplights:

I took the new wire (ensure it is the same rating as the existing wire - if it's 14/2, go with 14/2 and so on...), loosend the clamps inside the old box, and pushed the chunk of new wire out through my new opening. Fed the wire into the new box (knockout whichever hole tab is closest) and began to place the box into the hole

You can see that the top and bottom 'tabs' are hinged, so that they collapse inward to allow the box to slide in. Once you tighten the hold down clamps, the box ends will swing out and engage the tabs from beind. Tightening of the four screws on the outside edge of the box will snug up the tabs that sandwich the drywall and give a firm hold.

Ground your box with the bare copper wire, and trim the black/white to a length that is about two end-to-end folds (inside the box) long. Strip, being careful not to nick or expose the insulation. In my case, I threw in an old X10 outlet, so I didn't take photos - but for a regular outlet, bend the exposed wire with needle nose pliers (or the proper tool) to round the wire end to sit beneath the receptacle screws. Black to brass screw (Line) and white to chrome screw (neutral - should be the 'fat blade' plug). Your wiring may differ, so ensure that your existing wiring colors were done right and to the Code that applies to your jurisdiction. The plug checker tool that was mentioned earlier in the thread can assist with that.
If there is any doubt as to which wire is which - consult a professional. Bad wiring can kill, and no home project is worth a family's safety.
Reaching maximum image limit......moving on to part II....