To remove baseboard, casing, and jambs without causing damage to walls and splitting it with prybars, basically take a hammer and nail set and drive the nails on through the baseboard, casing, or jamb. Score any edges with paint/wallpaper with a razor knife before pulling the trim loose so you don't take any paint or wallpaper with it. When board is removed, then pull the nails or drive them on in. With stained wood, look for the spot of wood filler. Painted wood may need a little scraping. With either if it is still held and you can't find the nail, get a stud finder (the kind with a long magnet on a swivel that cost a couple bucks at walmart) and run it over the surface to find the nails. The nail head will be under the middle of the magnet.
To reapply use a larger finish nail and you should be able to use the same holes, angling nails if necessary, (or just make a new nail hole), and then fill holes with colored filler. Touch up finish as necessary.