Remove the door from the hinges with a screwdriver and lay the door on a flat surface with the interior of the door facing up.
Remove the old glass by scraping the old glazing compound away from the interior edges of the glass piece with a small putty knife. Press the putty knife into the base of the compound, where the compound covers the edges of the glass, at a 45 degree angle to remove the compound. Wear heavy gloves and eye protection in case the glass breaks.
Remove the old caulking residue from the interior side of the glass recess by scraping the residue away with a chisel. Insert the tip of the chisel into the recess vertically and press the chisel into the residue to lift the residue out of the recess.
Apply a coat of latex primer to the glass recess with a fine-tip paint brush to prevent corrosion.
Measure the distance between the sides of the glass opening and the distances between the top and bottom of the glass opening with a tape measure, then subtract 1/8 inches from each measured point and have a new glass piece cut to these measurements.
Apply a bead of caulking to the entire length of the glass recess with a caulking gun and press the new glass piece into the caulking.
Press new glazier's points into the putty with a putty knife. Space the glazier's points between 8 and 10 inches apart. The glazier's points are designed to help hold the glass in place.
Roll 3/8 inch strips of glazing compound between your hands and press the strips into the joint between the glass and the frame.
Smooth the glazing compound by dragging a putty knife across the compound at a 45 degree angle, then remove any excess compound with the putty knife. Allow several days to pass before reinstalling the door to allow the compound to dry.