Repair small damaged areas with solvent based filler for stained doors, or auto body putty for painted doors, with the door intact. Use a flexible putty knife to fill the damaged area with wood filler, until it is a little higher than the surrounding area. Mix auto putty one part hardener to six parts putty and apply in the same way to fill chips and small cracks. Allow the filler to harden according to the label instructions.
Sand down the filler with a power sander and 150 grit sandpaper until the surface is smooth and level with the surrounding area.
Apply stain and finish all-in-one in a matching color to stained doors, or semigloss latex paint to painted doors. Visually match for color using paint or stain samples from the finish retailer. Spread finish with a soft, fine bristle brush, working with the grain. Spread it using straight, even strokes, to prevent runs, drips or bubbles in the surface.
Allow the finish to dry according to the label recommended drying time. Apply a second coat to the area, feather the edges into the surrounding area to blend the repair into the door.
Remove the door from its hinges by driving the hinge pins up through the hinges with a screwdriver and hammer. Lift the door from the frame and lay it flat on sawhorses.
Drive a wood chisel into the joint between the end horizontal rail at the top or bottom, depending on the location of the damaged panel. Gently tap in the chisel with a hammer to widen the joint. Slip a flat pry bar into the joint to widen it further. Do this on both sides until the end rail is loose from the sides.
Tap the end rail with a rubber mallet toward the end of the door until it pushes out of the end. Tap the side stiles from the inside out to spread them until the panel can be pulled from the door.
Apply glue into the split in the panel. Use rubber padded quick grip bar clamps to press the spit in the panel closed. Wipe excess glue with a damp rag. Allow the panel to set overnight. Remove the clamps.
Replace the panel in the door, leaving it loose to expand and contract as needed. Apply glue to the ends of the end rail. Tap the end rail back into the door until its outside edge is even with the ends of the stiles. Press the stiles back together with pipe clamps. Allow the door to set overnight. Realign the hinges and tap the pins into the hinges with the hammer.