Back out the sheet metal screws securing the gutter to the downspout with a drill and Phillips driving bit. Gently lift up each shingle that has a gutter hook secured to the roof underneath it. Use a pry bar to pull the hook's nails out the roof. Once all hooks have been removed, ask a friend to help you lower the gutter to the ground.
Insert a pry bar behind the fascia board at one end. Pull the pry bar forward to separate the fascia from the eave or rafter tails. Check that the eave or rafter tails behind the fascia have not become soft or moldy. Work your way along the house to remove as much damaged fascia as necessary.
Measure along the eaves or rafter tails to determine the length of new fascia you need. Transfer this measurement to a new piece of fascia and cut it to length with a circular saw. Set the fascia on two sawhorses and prime the entire board with a high-quality exterior primer. Allow the fascia two to three hours to dry.
Lift the new fascia board up to the eave or rafter tails. Hammer a pair of 8d galvanized nails through the fascia and into each rafter tail or every 16 inches along the eave. Use a 1/2-inch putty knife to spread a thin layer of wood putty over each nail head.
Hook a chalk line over one of the fascia board's ends and extend it toward the other end. Look for areas of the fascia that seem to bend in. Hammer wooden shims behind the fascia to help push out these areas and hold the fascia even.
Ask a friend to help you lift the gutter back up to the roof. Lower the gutter's ends onto the downspouts and use the sheet metal screws you removed in Step 1 to hold them together. Secure the gutter hooks back underneath the roof shingles with galvanized nails.