how can i repair my wood shed roof?

Yeah cut a square/retangle opening back to undamaged area batten around the edges inside to form a rebate for new panel to sit on. Screw these battens from the outside so any screw tips will be inside and cause no damage to new shingles. Cut the new panel from marine ply but leave an approximate gap of 1/8" all around the opening to allow for expansion. Apply flexi,none setting, mastic to the battens press the ply in place and screw it down. Then mastic the 1/8" joint smooth flat, then mastic over all screwheads. Re-shingle as required.
job done.
From Bob the retired repair man.

Bob UK
August 2009

Sure - just use an exterior quality plywood, and preferably put an underlay felt down before you fix the shingles proper.

John
August 2009