Things You'll Need
Metal drill bits
Rust seems to affect everything it can, and its effects can be seriously damaging. On older homes, or ones with older hardware, rust can show up in the strangest places, including door hinges. At first, that doesn't seem like a serious problem; but if the hinge continues to rust, the door will eventually fail, and could even harm the person opening it. The first step in fixing a rusty hinge is removing it, and that can take some time and cause a little bit of frustration. But once it's done, you won't have to worry about the door again.
Open the door and position yourself to access the lowest hinge in the door. Start at the bottom so that the door can stay hanging off at least by one hinge.
Place the center punch in the middle of the screw on the door and strike it with the hammer. This is going to create a point for you to place the drill on later, so the bit doesn't wander.
Insert a small drill bit--1/8 inch or less--inside the drill and place the bit on the center punched mark. Drill out the center of the screw using progressively larger bits until the screw is completely gone.
Repeat steps 2 and 3 for the other hinge screws mounted to the door, working your way up until you've removed all of the screws from the hinges and the door is off the hinges.
Repeat steps 2 to 3 for the screws holding the hinges to the door jam. Then remove the hinges from the jam using your hands.
This article covers removing the hinges, but if you want to stop rust from forming in the first place, consider using stainless steel hinges for your replacement. Stainless steel won't rust, and it also provides a modern aesthetic.
Check for rust periodically, and scrub it off before it becomes a problem. This will prolong the life of your hinges.