Start two rows of shingles above the top holes you drilled from inside and insert a flat prybar between the shingles to break the seal. Slide the bar and remove the roofing nails that attach the shingles. Try not to cut any of the shingles. Remove entire shingles pieces, or it may look like a patching job when you re-shingle around the skylight.
Work from the top down and remove enough shingles to work around the skylight, but do not remove the last row of shingles where you drilled the bottom holes. You will be setting the flange of the skylight on top of these shingles to allow for water drainage.
Remove any roofing nails left behind from removing the shingles.