Inserting Glass Pane in Wooden Door
Glass is heavy and many wood doors are not constructed to bear the weight of the glass. You should look into using Plexiglass. It's  third of the weight of glass and most home stores will cut it to size. You'll have to buy the whole sheet.
Try to remove the panel molding off one side of your door and then remove the panel. Get an exact measurement for the Plexiglass, install it and replace the molding.