Piece together the damaged wood by placing the splintered pieces back together as best you can. Remove any splintered pieces that are sticking out or damaged too much to be a part of the door.
Sand any rough edges of the splintered area using sandpaper to smooth the surface of the door.
Place some wood glue along the damaged area to hold the wood together if it is loose. Then use a power drill to drive wood screws into the damaged area as well as just above and below the damage. For simple splinters, this step can be skipped, but for doors with extensive damage, that have been kicked in for instance, screws and wood glue will make the door structurally sound again.
Place wood putty over the area after the glue has had time to dry. After the putty has dried, use sandpaper to sand the door down and make sure the area is level again.
Use stain or paint to color the damaged area to match the rest of the door. In some cases, you may have to stain the entire door if the door is weathered from the original color.