Plug the device that’s having problems into a different outlet, in a different part of the house, to confirm that the problem is with the device. If the device works when you plug it into another outlet, ensure that your circuit breakers are all in the “on” position and that there’s not a problem with a particular wall outlet.
Plug a different item that you are sure works, such as a lamp with a bulb that you've ensured works, into the outlet that the prior device was plugged into. If the lamp or other item works, the problem is not with the electrical outlet. If the lamp won't light, you can assume the outlet is faulty. Try the working lamp in the outlet's other female adapter to see if both have failed.
Unplug the device's cord from the wall outlet. Inspect the entire length of the power cord for cuts and nicks, and for any exposed wire. Check for loose connections as well -- both where the plug attaches to the cord and where the cord attaches to the device. Repair or replace the cord as necessary.
Look carefully at the plug itself. All prongs should be straight and should fit snugly into the outlet. If the plastic casing of the plug is melted or scorched, this indicates a short-circuit inside the plug, and the plug should be replaced.
If possible, open the plug using a screwdriver. Some plugs have a small plastic piece in between the prongs or on the side of the plug opposite the prongs that's removable. Verify that the wires inside are securely screwed down to the respective post for each prong. The exposed ends of each wire should not touch each other. If they do, redo the connections before reassembling the plug.
If checking the plug does not fix the problem, swap the cord with another one, if you can easily unplug the cord from the back of the device. For example, many computers, televisions and other electronics use cords with a female plug that attaches to the back of the device; these cords are interchangeable.