Stick an awl directly into the rotted corner framing to determine the severity of the wood rot. The deeper your awl goes into the wood, the more severe the problem. Remove all rotted wood by lifting up with the awl.
Inspect the general area for any issues causing the wood rot. Common problems include leaking pipes and general exposure to the elements. Fix these problems before you continue.
Drill several holes into the rotted area with a hand-held power drill. These holes serve as an anchor for the epoxy consolidant. Drill about halfway through the lumber.
Mix the epoxy consolidant with a putty knife and apply directly over the damaged area. Use the putty knife to spread the epoxy as evenly as possible. Use a syringe to fill the drilled holes with epoxy. Allow the epoxy to dry.
Apply a thin layer of epoxy filler over the dried epoxy consolidant to help you reshape the the lumber, if necessary. Use the putty knife to apply the epoxy filler and allow to dry after application.
Sand down the work area with a sheet of sandpaper until you sand the epoxy filler even with the rest of the lumber.