Remove the door from its hinges, and remove hardware from the door, including the doorknob, door knocker and hinge brackets. Use a screwdriver. Set aside the hardware to put it back later.
Lay a tarp on the ground, and place a sawhorse at each end of the tarp. Lay the door over the two sawhorses. If no sawhorses are available, find a work table, or lean the door against a wall and work on it that way.
Sand the door with a 60-grit sandpaper. This will remove any finish over the stain and the stain itself. Continue to sand the door with progressively finer grades of sandpaper (100-, then 150- and then 220-) in order to smooth the marks from the rougher sandpaper.
Tape the edges of any windows in the door, using painters tape.
Prime the door. Use an angled sash brush to paint paneled areas and a flat brush to paint flat areas. If the door is flat, use a roller. Exterior grade primer should be used for exterior doors. Allow the primer to dry.
Fill any cracks with caulk or putty, and allow to dry.
Sand and then prime the repaired cracks.
Paint the door in your chosen color, and allow it to dry. Paint a second coat over the first coat if necessary. Continue to paint coats on the door until the finish is even — for some colors, this could take three or more coats.