Pick a dry day above freezing and remove all the old material. Start at the bottom and work up overlapping seams of the flashing by about 6" or more. Clear caulk applied to all seams on the flashing. Then replace the shingles bottom to top and caulk all nail holes.
You can't really repair shingles since they are solid. Purchase some new shingles, flashing, and roofing tar. Make sure the flashing fits under the new shingles and tar around the flashing so no water can leak through.