If just the actual trim, rather than the 2x6 or 2x8 or 2x10 frame, easy to do yourself, or a handyman or finish carpenter can do it. If you are talking a damaged frame, you should probably use a carpenter unless you are moderately home handy. Cheaper if you prime and paint it yourself.
If just the "stop" trim (about 1/2-3/4 thick by 3-6 inches wide) that the door face butts up against, that is justed nailed on with finish nails - easily pried off with a small prybar or flat tip screwdriver, new one nails on with 5-6d (5 or 6 penney) casing or siding nails or 6d finish nails (nails with small nub heads rather than big flat heads).
If you do it yourself cut or break off a small piece to take to building supply store or yard - is a standard stock item.
When you put it back on you can line it up with the paint mark left when it came off, or with garage door closed, press it up against the door (in contact, not hard enough to move the door away) and nail in place. It should fit flush at both ends to help stop rain and insect penetration, except at the bottom it is better practice to leave it 1/4" clear of the ground and caulk that gap, so it is not touching sometimes wet concrete and wood boring insects.
For exterior trim I would use an exterior oil-based primer though some people do not take the time to do that, and after a good solid day of dry air conditions put on 2 coats of an exterior oil or acrylic latex door and trim paint per instructions.