If the power supply to the microwave is fine but nothing is comming on then its more then likely the internal fuse thats blown.
As microwaves have an internal fuse in there so if this blows it cuts the power out in there. If you are looking at fixing this yourself the you need to remove the microwave and then remove the outer casing. Locate the circuit boards and the fuse is located on there. Is usually a small 8 amp fuse. You will need to replace this and fingers crossed its just a fuse only. But if it goes again then something in there is causing this.
But when repairing microwaves you must be very carefull as they can store very high voltage even when unplugged. They can store upto 4500v so you must discharge the high voltage capacitor at the bottom before touching anything in there.
So check that fuse if you can and fingers crossed its just that at fault.
You either need a discharge lead which i take it you wont have.
So in this case you need a well insulated handle big screwdriver and touch the wires on the capacitor to the metal cabinet and that will discharge it.