Cut out the damaged area into a clean, regular shape
Trace the cutout onto matching replacement material
Cut the patch slightly oversized
Trim the patch to fit the opening with tight, even edges
Test-fit the patch until it sits flush
Apply adhesive, epoxy, or sealant as appropriate
Insert the patch into the opening
Clamp or hold the patch in place until set
Fill any small gaps with matching filler or caulk
Sand the repaired area smooth
Finish with stain, paint, or topcoat to match the surface