Tear out the cross bracing members, cutting the nails with a reciprocating saw if necessary. Take off the screen door, stops and hinges. Remove the screen studs and save them for framing the door openings. Just to be sure, measure all the new rough openings and adjust any of them that don't match up. After that, cut out all the bottom plates in the rough openings.
Test fit the door frame in the rough opening.
Once it fits correctly, remove it and caulk along the bottom. Fit the frame into the opening and step down to seal the caulk. Then nail the lower corners down. With a level against one jamb, make sure the sides are plumb and nail the top corner in place. Continue down the side plumbing and nailing.