How can I locate and repair a break in a circuit?
Locate the serviceable junction immediately upstream of nonfunctional outlet.
Establish which wires go to defective socket.
Switch off house mains and make safe.
Disconnect these upstream wires at the junction.
Disconnect downstream defective socket.
Using a long length of bell wire, attach it to the disconnected wiring at upstream junction, and bring the free end to the vicinity of defective outlet. Then with a continuity tester, check for continuity between upstream junction disconnected wiring and disconnected wiring from defective outlet.
This will establish whether a discontinuity exists in any of the wiring between upstream and outlet.
If no discontinuity exists, then the wiring is sound, and you need to then explore all wiring connections as described elsewhere in the other answers.
If one exists, then examine the suspected route of the wiring and look for a possible intrusion, a nail or screw, or evidence of one having once been there (a hole, or a repaired surface). That would probably be your culprit.
If you can expose the wiring in that area, locate the break, and contemplate an in-line splice at the fault. (This is what I did, with success, and the repaired area of decorative finish was small and easily disguised.)
Of course, if your wiring is within conduits, then the easy repair is to tie string (or replacement wiring) to the wires at the outlet then haul the wiring back to the upstream junction and use the string (if using) to install the replacement. Before hooking everything back up, conduct another continuity check to make sure the new wiring has no breaks.