How to Clean a Bathroom Fan

Turn off the power.

Remove the cover. Most covers have 2 prongs on opposite sides holding it in place, others just need to be unscrewed. Remove the cover by pressing these prongs in or removing the screws, then set the cover aside.
Remove the fan. Unscrew the assembly that is holding the fan in place, then very gently remove the fan.

Clean the cover and fan. Start by vacuuming off the majority of the built up grime on both the cover and the fan. Then dip a rag, preferably a microfiber cloth, in soapy water and use it to wipe up the remaining dust. Vacuum the exhaust pipe. Use a crevice or brush attachment and vacuum off the inside of the exhaust pipe. If you can reach, also use your rag or cloth to wipe off what the vacuum could not get.

Vacuum the external exhaust port.

Wipe and vacuum the fan housing.

Put the fan back in place. Before reinstalling the fan, make sure that you cleaned off all the dust from in between each of the blades and dried it thoroughly. Carefully reinsert it into the exhaust pipe and screw the bracing back into place.

Turn the power back on.

Reinstall the cover. Once the cover has dried, either screw it back in or bend the prongs until the cover snaps back into place.