Wood patch with epoxy and fiberglass

From KayakWiki

If aesthetics are important (which they often are to wood boat paddlers), rather than making a solid fiberglass repair, like a epoxy and fiberglass patch wood is cut to fill the hole and match surrounding wood, with fiberglass re-applied to protect the new wood.

Drying the kayak
Make sure the kayak is allowed to thoroughly dry. Water can wick quite aways back into the wood structure of the boat, so a week or more in dry climates, and 2-3 weeks in humid climates may be necessary. Sitting the kayak in the hot summer sun will speed up the drying process, as does placing a fan in proximity to the patch to circulate drying air.
Cleaning the hole
If all the original wood is still present, and not terribly damaged, it may be re-used in the repair, rather than chancing replacement wood not matching the original. If this is not the case, Clean the hole as with a epoxy and fiberglass patch. Try to press all the wood fibers back in place. If this can be easily done, proceed to gluing the wood together. If there is a lot of resistance, try cutting any offending splinters that may be keeping the plug from lying back down.
Cutting new wood
If you are unable to repair the hole with original wood, you will need to cut a clean hole around the damaged area so you will have an easy surface to match and glue to. Following the lines of the strips on a strip-built kayak will help to hide the patch. Cutting an irregular-shaped hole in a plywood kayak will help, but remember that the irregular shape must be matched with the repair plug.

Cut strips or plywood to match the hole. Holding them outside the hole, and tracing along the inside of the hole may help. Remember to cut slightly outside the lines to account for pencil thickness.
Gluing the wood together
Coat both the plug and the hole with unthickened epoxy, and then brush on thickened epoxy. Tape in place. If you are regluing the original wood in, you may need to cover the wood with plastic wrap and place a small piece of plywood over the plastic wrap. Clamp or wedge the plywood against the repair to keep the wood lying inside the hole.
Fiberglassing
Cut 2 pieces of fiberglass 2" larger than the plug. 'Glass one inside the repair, and one outside. When cured, feather the edge of the glass so it transitions into the surrounding fiberglass. Recoat with epoxy. Sand smooth. Recoat with epoxy again. When epoxy cures, scuff-sand with 220 grit sandpaper and re-varnish.