Put on work gloves and safety glasses before your begin.
Slide a putty knife between the trim, or mull, on the door and the frame. Push back on the knife to open a space in the trim and slide in a pry bar. Use the pry bar to pull off the trim.
Pick out any glass shards that come free easily once the mull is off. If glass sticks in the frame, pry off the caulking with the putty knife to free it.
Apply a bead of caulk around the inside edge of the door. Slide the replacement pane into the groove of the frame.
Add a second bead of caulk at the intersection between the glass and the frame. Press the mull over the wet caulk, starting in one corner and working your way around.
Wipe off excess caulk with the putty knife. Once the caulking cures, wipe the glass down with window cleaner and paper towels.