Remove the window from the garden outbuilding by prying the stops that hold the window in place off. Use a flat bar to work the stops up until they can be pulled out. Remove the finish nails with pliers.
Remove the window from the opening and place it on a work surface. Clean off any loose paint and debris with a wire brush. Sand the wood smooth with sandpaper.
Scrape out the glazing putty around the window pane with a putty knife. Work around the edges to carefully loosen and remove the putty.
Pry out the glazier points with the tip of a flat-head screwdriver. Be careful not to put pressure on the glass as you pry them out. The points hold the glass in place.
Lift the window pane out of the window opening. Lightly wire brush the wood underneath the pane to create a smooth surface.
Mix the epoxy primer with a putty knife and apply it to the damaged area of the wood sash with a poly brush. Allow the primer to set up for the directed amount of time. Mix the epoxy filler and apply it with a putty knife. Allow the epoxy to dry. Sand the repaired area flush with the surface of the wood.
Apply a bead of caulk around the area of the sash where the window pane sits. Insert the replacement window pane into the window opening. Press it against the caulk.
Tap the glazier points into the wood to hold the window pane in place, using a tack hammer. Insert the points from each place along the pane where you removed one.
Re-glaze the window pane with glazing putty and a putty knife. Create a smooth transition in the corner from where the glass meets the window sash to the front surface of the opening. Allow the putty to dry.
Apply a wood finish to the repaired garden window. Allow the finish to dry.
Insert the window into the frame in the outbuilding. Reinstall the stops with finish nails and a hammer. Drive the nails through the existing holes in the stops.