The quick answer is replace the damaged wood but that is not enough. I recommend installing a product such as Blueskin over the new wood. Blueskin is a plastic film material that sticks to the wood and water can not penetrate.
Also, if possible a storm door or overhang/porch will provide additional protection for the exterior door. But many times these options are not practical.
I am a full-time home inspector servicing all of South Carolina.