After some effort, I have determined that there is a discontinuity between the wire from the breaker (hot wire) and the receptacle (socket). The breaker is okay because couple of other sockets in the same circuit are working. However, several sockets downstream from this socket are not working, i.e., are dead. The wiring in question comes from attic, through the wall (stud) and finally to the receptacle. Before I fix anything, how do I make sure that my diagnosis is 100% correct. If correct, how do I fix this wire or replace the wiring without breaking the sheet rock of the bedroom wall?
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.
I had no argument with most of the diagnosis and suggestions posted here. But the fact remains that each case may be different. Mine certainly was different. After spending every neuron of my brain, every gadget I could find, borrow, or buy, the final diagnosis was was that what I had initially suspected. There was a discontinuity (i.e. break) somewhere in the middle of the wiring, not at a junction. Some of better electricians won't and don't need to believe it. Eventually I had to cut out, pull out, and rewire about 20-25 ft. of wiring from one location to the receptacle (socket). I, the house lady (my wife), friends (who helped) and a handy man (electrician) were pleasantly surprised. This was more of the case of "Murphy's Law." "Anything that can go wrong, did go wrong." Sometimes it is the 1% that we don't think about may be the case.
I'm going through this exact same problem. The hard and time consuming part is to literally check every connection, twist-on connector, or otherwise. Use a volt meter to check for live service once you have it all opened up. Put it back together, check to ensure it's working, then move on to the next one.
Eventually you will find the broken component. Tedious and time consuming.
Good luck to both of us.
The pro answer is a circuit tracer, which has a transmitter you plug in or clip to the dead wires and uses them as a transmitting antenna, and a receiver which lets you follow that wire back thru the walls; when you find the place where the signal stops, you've found the break (or switch or whatever). It's the big brother of the "breaker finders" commonly available, but the transmitter is powered by a battery rather than by the line, and it puts out a clearer signal.
I had to get one (was able to borrow, luckily) when my contractor cut thru a wire and their electrician didn't know about these tools. They can probably be rented too. They're expensive to buy new, but sometimes they turn up used on auction sites.
Electricity is generally transmitted to the house from the transformer either on a power pole or on the ground in a transformer box. The power company attached to two black wires and a ground to bring 240 volts into your meter. Then the wires go from the meter into your house. The two black wires connect to your main breaker which can be 100 to 400 amp service. This in turn makes the panel buss hot. If you have one breaker it provides 120 volts of electricity throughout one circuit. If there are two together or a breaker that takes 2 positions, then this is a double pole breaker 240V. For this question we focus on the single breaker with a black wire attached to it. The two wires: hot (usually black in the USA) and neutral (white in the USA). An outlet not working can be caused by either (or both) of these being disconnected.
The tools normally used for diagnosis are a voltmeter and a non-contact voltage tester (rated for the proper voltage, usually 120 or 240 V depending on the country).
The most likely cause is a bad connection. Modern electrical code requires all connections to be in accessible locations inside some sort of electrical box, so you should be able to find all of them. It is likely that the bad connection is a "back-stabbed" wire, which is where a wire is inserted into the back of an outlet and a weak spring holds it in. The "back-wire" outlets where a bolt holds down the wire is good and suggested.
Assuming that there is a ground in your outlet, measure the voltage between ground and the two other prongs. If ground->hot is 120/240 V +/- 10%, then the hot is "good". If neutral->ground is very close to zero volts, then the neutral is "good". This will let you focus your inspection efforts. You can also use a non-contact voltage tester to test the hot. If it says the hot is hot, your problem is with the neutral, but if it says the hot is bad, then you won't really be able to tell if the neutral is also a problem.
Turn off your circuit using the breaker, verify that the power is turned off in the outlets that you'll look at, dismantle the problem outlet and the neighbours, and inspect the connections. Make sure that there's no burnt plastic, replace outlets if they're no longer holding plugs, and check the connections. For wire nuts, try to pull the wires out of the nut, and reconnect them if they pull out. Change back-stab connections to side/back wire for better durability. Tighten any loose bolts holding down wires.
If it isn't a connection problem, it'll have to be a problem with the wire or possibly the outlet in question. Pull out the problem outlet, turn the circuit back on, and use a voltmeter to check if the wires going to the outlet are properly energized (Verify the neutral->hot voltage is as expected). If this shows the wire is bad, you will probably need to fish a new wire through the wall (and remove the old, broken wire).
Remember, working with live circuits is dangerous, and turn off the circuit before making any modifications to it or actions where you could touch the wires, or short them together.
Actually, it is probably a loose wire nut inside a box. This is much more likely than a broken wire.
Figure out how the wiring runs from one receptable to another. If you know all the receptables that are working and all the ones that aren't, you can probably guess the where the suspect connection is. Then open up the boxes at either end of that connection. I would bet that in one of those boxes, a wirenut is loose. Probably it will be obvious what the problem is. If it is not obvious, then either use a non-contact voltage detector (carefully), or just unfasten and refasten all the nuts.
If this doesn't work, then maybe there is a junction box in the path. Repeat at that location. If this does work, THEN I would start suspecting the wire itself.
Cheap cable tracer is available at harbor freight for $25 http://m.harborfreight.com/cable-tracker-94181.html