Score along the seam with a utility knife where the top edge of the riser and bottom edge of the stair tread adjoin along each stair riser you need to remove. Scoring the seam will break any seal formed by the wood finish.
Slide a putty knife between the stair tread and riser joint along the stair riser to lift the tread up just enough to slide a trim flat bar into the joint.
Slide a flat trim bar into the joints and pry the stair treads up. Lift up along the entire stair tread with the flat bar and pry each tread up. Set the stair treads aside. The top of the stair stringers are now exposed so that you can remove the risers.
Tap the flat bar between the stringers and risers with a mallet. Pry out on the flat bar on each end of the risers and lift them from the stringers.
Pull out the nails from the back side of the treads and stringers with a nail puller. Pull out any nails left in the stringers with the nail puller to prepare them for the new risers.