Old glass door knobs are generally part of a mortise-lock system. Unlike self-contained modern latching systems, the knobs in mortise systems are separate from the latching mechanism, and are interchangeable with other mortise systems. This means you can take out the knobs and their spindles (the square threaded brass piece between the knobs) and replace the spindles and screws as needed, without affecting the rest of the latching system
Things You'll Need
Small standard screwdriver
Open the door part way. Brace your feet on either side of the door, to hold it steady.
Set your screwdriver head into the slot on the small screw at the base of the glass knob. Hold the knob still with one hand while turning the screw counterclockwise with the other, loosening it. Loosen the screw about halfway, but don't take it completely out.
Hold the other doorknob steady with one hand. With your other hand, turn the first doorknob counterclockwise. It should unscrew from the screw-threaded spindle (if it doesn't, then loosening the small screw at the base some more). Take the knob completely off.
Pull the other doorknob out from the door. It will pull away freely, pulling the spindle out with it.
Loosen the small screw at the base of the second knob, as before. Clamp a pair of pliers over the middle of the square spindle and hold it tight while your twist the knob counterclockwise to remove it from the spindle. The knobs are now ready for re-installation with a new spindle.