To repair a patio door screen, take the handle off the screen, take the spline and screen out of the frame, and take the rollers out. Set the new screen in place using a convex roller to push the screen into the groove of the frame. Set the spline in place using a concave roller, and cut off the excess screen material. Reinstall the rollers, and put the screen back in place.
The spline usually consists of four separate pieces, one on each side of the door frame. Lift up each end of the spline pieces, and carefully pry them up. If they aren't damaged, you may set them back in place after repairing the screen. If you choose to install a new spline, make sure its diameter and length are the same as the old one's. Use a sharp utility knife to remove the excess screen material, and make the cut between the spline and outside edge of the spline groove.
If the rollers on the screen are broken, install new ones. To do so, insert the roller assembly into the opening in the rails at the end of the door, and secure them with clips. You may need to install a new screen panel. Insert it into the door track, and adjust the screws until it starts closing evenly against the jamb.