This is a somewhat common problem. Your door is out of alignment.
Rather that replacing the door hinges you can try loosening the upper hinge and use a hammer against a solid peace of wood moving the hinge forward an eighth of an inch. This tightens the hinge and lifts the door enough to avoid that annoying problem when chipping the paint on the top corner of the door. Really, the hinge should be replaced but this should hold for while and only takes five minutes. This is a temporary fix.
Ok, lots of older cars have a problem with hanging doors. You have two options on how to fix this. You can replace the doors or the hinges or both. If it's hanging only replace the hinges, 1 upper and 1 lower per door. Now, if your door is rusted you may want to replace the entire door.
First, you need to look at the bottom of the door and see if it's rusted out. The doors should be completely solid down there with no holes or flakes. If there is, then it's rusted. If it's not rusted bad, you can leave the door the way it is if you like. If the rust is bad (if you can drop something in the top by the window and have it fall through), you may want to replace it.
Second, if you opt to replace the door(s) you need to find a rust free door for your car. The old door must be taken off, use an air-compressed torque-wrench to get at the bolts.
Third, have someone hold the door open (use a jack, too) while you remove the hinges and remove the door. Then with the new hinges you got already (you knew that, right?) take 'em and bolt 'em on to the new door. If the new door has hinges that look in order, you can use these. New hinges are recommended though. You may as well replace 'em while the door's off.
Fourth, have someone hold the door again while you line it up. It's also useful to use a jack of some sort, or some type of immobile support to hold the door in place, but have a person hold it for steadiness. Connect the top bolts, do not tighten completely. Connect the bottom bolts, again do not tighten completely. Make them snug. Remove the supports and shut the door gently (remember the bolts aren't 100% tight).
Fifth, while the door is shut, check to see if the "crease" where the front of the door meets the bode is even. Also, check the bottom of the door for alignment to the body. If it needs to go up or forward a little, you've gotta open up the door and while one person looks at the hinges, the "adjuster" moves it forward or up or whatever's necessary. When you think you've got it, tighten the bolts to the frame.
Sixth, if you lucked out and got it lined up right the first time, you're done. Otherwise, continue step five until you've got it to where you're happy with it. The doors should now shut like new. Grease 'em up and you're good to go (to the body shop to get the doors painted to match the rest of the car).
Now, if you're just replacing the hinges, that's a little simpler.
First, support the door with a person and a jack of some sort while it's open. Remove the bolts that connect the upper hinge to the frame of the car. Then you should be able to move the door a little and remove the bolts that connect that hinge to the door.
Second, throw the old hinge across the room 'cuz you're pissed off you have to do this. Then take the new hinge and bolt it in where the old one was. Make sure that you are bolting in another upper hinge (as opposed to lower).
Third, do the same for the bottom hinge as you did with the top hinge and go to step four.
Fourth, see step five in the above section ("New Doors") and follow that until completion.
Here is a video I found - Sagging hinge repair on Lincoln Town Car