All good info given, but this kinda parallels the 'what car you working on?'question.
How old is the wiring. Do you have breakers or fuses? Proper grounds to the outlets (three conductors). GFCI?
Most likely a simple outlet change will solve the problem. If it didnt pop the breaker/fuse there is not likely to be a short. Connections loosen and arc = poof. Still good to verify as much as possible. Safety test for AC voltage on both black and white to ground before working on it.
If you have 'modern' grounded system and no GFI, you may want to upgrade to improve safety. If there are multiple outlets most GFIs will protect regular outlets beyond them in the line. I have run into some old boxes that are too small to fit a GFI, but they do make smaller ones that fit most- still very tight.
Black is 'hot' and always goes to the brass screw. White to silver.