Guitar pickups are part of a guitar's electronic system, and their purpose is to pick up the sound generated by the strings — hence the name. Over time, pickups can become corroded from humidity or even acid from your hands. This will show up as rust spots. It takes a lot of rust to effect the sound quality pickups produce through the amplifier, but keeping them clean will prevent it from building up enough to interfere with your music.
Unscrew the pickups using a screwdriver or hex wrench and set the screws aside. Hex wrenches, also known as Allen wrenches, come in sets of various sizes and will remove most pickup screws and other guitar hardware. Use a screwdriver if you do not have hex wrenches and if the screwdriver will fit your screws. A screwdriver or hex wrench that fits properly will not strip the screws, so they remain in good condition and you can use them again.
Remove the pickup face plates carefully. Leave everything plugged into the guitar electronics and do not pull any of the wiring out of place while you work, or you may damage the connection, which could require you to reattach or even re-solder wires.
Remove the rust with a rust cleaner. Use a cleaner that includes a rust-dissolving agent such as oxalic acid. Apply a small amount of rust cleaner to a soft cloth and use the cloth to rub away any rust on the pickups. Do not pour the rust cleaner directly on the pickups.
Polish the pickups with a clean, soft cloth. Rub the pickups gently with the cloth to remove any rust-cleaner residue and restore the pickups' original shine. If the screw holes are prone to rusting, you can apply a small amount of clear nail polish to inhibit it.
Place the pickups back into the guitar. Once they are positioned properly, screw them back in. Replace screws if they are rusty rather than trying to clean them; since screws are inexpensive and widely available, cleaning them is often more work than it is worth. If your old screws are still serviceable, wipe them with the polishing cloth or a clean rag to remove dust and screw them back into place.
Do not use steel wool to remove rust from pickups. Steel wool leaves tiny pieces of the wool behind. These get caught in the magnetic part of pickups and may interfere with function. It also makes the pickups look even dirtier than when you started.