After the molding has been removed, turn off the power and cut away the wallboard, staying beneath the pencil line. Install the new box, drill holes through the studs, and pull cable from the existing receptacle to the new one (leave about 6 in. of slack in each box). Connect the old receptacle to the new one, then replace the cut-away wallboard, and reinstall the molding.
If you need to wire around an existing door but don't want to cut away all the wallboard above the header and can't get through the attic or basement, run the cable through the shim space around the door. Remove the door trim and the baseboard molding. Turn off the power and pull the cable through the studs and the shim space. You'll have to chisel the shims enough to fit the cable and then protect the cable from nails and screws with 1/16-in.-thick metal plates. After running the cable, reinstall any wallboard or trim you removed.