Spray a water displacement aerosol, like WD-40, or a liquid oil lubricant onto the hinges then open and close the door several times so it seeps in. This will stop the hinges squeaking, but will only be temporary.
Remove the hinge pins from the hinges. This may involve tapping the hinges from underneath with a hammer so the pin falls out, unscrewing the hinges from the door entirely or the removal of the entire door. The hinge pin is the metal tube running thought the middle of the hinge. This may sound like a hassle, but can be done in a few minutes.
Rub the hinge pin with a piece of wire wool to remove any rust and inspect the rest of the hinge for additional corrosion. Remove as much rust as possible from the rest of the hinge using wire wool.
Apply both a water displacement aerosol and lubricating oil to the hinge and the hinge pin.
Reassemble the hinge and reattach to the door.