In my house, which is rather old, the door hinges are stiff, and the cabinets don't close well. I need to install new ones.

It'll save you time and frustration. With the door closed and latched, remove the hinge pins by tapping on the bottom of the hinge pin with a nail and hammer. After pins pop up an inch or so ...

A simple hinge consists of two separate leaves, joined in the centre around a pin. The knuckles surround the pin and allow the two leaves to move – making a door or lid open and close.