Take the wood trim off of the door jamb with a putty knife. Insert the putty knife between the trim and the frame and gently pry out. Do not crack the wood. Take your time and slowly pop the trim off, section by section. Place the trim aside.
Remove the nails from the door frame. If the nails popped through the trim and are left in the frame, remove them with the back of your hammer. Place the nails in a bucket while you work; you can reuse them if they are not bent.
Plane the bowed wood in the jamb. Run the plane over the wood to shave it down. Use a level to check your progress. Continue planing the wood until the level reads that the entire jam is even.
Replace the trim. Hold the trim in place and nail it back into the door jamb.