Step 1: #1 Aerosol Lubricating Oil
Syringes are good for other things, not just injecting yourself with... substances. Or stealing someone's bodily fluids while they sleep. You can squirt some oil onto the hinges. Open and close the annoying door several times. The sending-chills-down-your-spine noise should be no more.
Important: Make sure the oil actually does penetrate the hinges. If you can't find a syringe, you can simply purchase a can of WD-40 (the paragon of penetration).
If this doesn't work, I have to say, Houston, we have a problem. Maybe your door is stubborn and won't surrender easily Or maybe it is haunted by your grandma's cranky ghost.
Step 2: #2 Remove the Hinge
Do you see the round hinge pin? It's role is to be between the flat plates and to hold them together. The next "big" task you will have to do is to move the pin clockwise and then counter-clockwise until you remove it. But don't try with your hands. Use the high-technological tool called pliers.
Important: Watch out with the slippery pliers or you may hurt yourself.