Remove any molding or pieces of decorative wood that are holding the soffit in place.
Draw lines along rafter edges nearest to the damaged area on either side of the rotted portion.
Drill a hole on each line to serve as an entry hole for the jigsaw.
Cut along the drawn lines using a jigsaw. Use caution when working with the jigsaw, especially on a ladder. Do not forget to wear safety goggles to protect eyes from sawdust and other debris.
Pry and pull the cut, damaged portion of soffit out.
Remove any bird nests or other debris from the now-exposed area and cut off any additional soffit if the initial removal has exposed more extensive rot on the upper surface of the soffit.
Measure the dimensions of the space where the soffit was removed from.
Cut a piece of exterior plywood according to the measurements but plan for about one-eighth inch of space between the new and existing soffit.
Nail pieces of scrapwood, like 2x2 or 2x4 blocks, to the rafters on opposite sides inside the opening, extending into the opening to provide a surface to attach the plywood to.
Screw the replacement wood to the nailed-in wood pieces and rafter using galvanized deck screws.
Reinstall any decorative trim or molding.
Fill joints, screw holes and any other openings with caulk.A silicone-based, paintable caulk is generally suitable for this application.
Prime, paint or otherwise finish the replacement panel to match its surroundings.