Unplug the microwave, and let it sit for a minimum of two hours. Move the microwave to a work table or area where you can gain access to the back of the appliance.
Remove the screws off the back panel of the microwave to gain access to the interior of the appliance. Set the screws aside so you do not lose them.
Connect the voltmeter test probes to the terminals on the capacitor to ensure that the capacitor has discharged. Look at the voltage gauge on the meter to determine the capacitor has no voltage flowing through the component.
Unscrew the side panels that surround the magnetron so you have full access to the component. Pull the connecting wires leading to the magnetron with needle-nose pliers. Write down where each wire connects so you do not forget which wire goes to which component.
Remove the screws from the base of the transformer, and remove it from the bottom of the microwave. Use the screwdriver to remove the mounting screws on the magnetron, and pull the component from the microwave.
Insert the thin wire with a soft cloth on the end inside the magnetron's case, and push through, dislodging any debris. Move the thin wire up and down or side to side to ensure the magnetron case is thoroughly cleaned. Blow off any dirt and dust with an air compressor hose, or wipe down the magnetron with a soft cloth.
Repeat the steps in the opposite order when reassembling the microwave. Insert the magnetron and the transformer, reconnect the wires, install the magnetron side panels, and screw the back panel back in place. Plug the microwave into an outlet, and see if the appliance works properly.