Check the caulk around the skylight on both sides of the roof. If it is loose or shriveled up, peel it away and apply a new bead of caulk around the skylight. This prevents both air and water from leaking through the roof.
Wrap aluminum duct tape around any joints on the skylight tube. The tube and its joints will be accessible from the attic.
Measure the circumference of the skylight tube.
Cut strips of fiberglass insulation to fit the circumference of the skylight tube, plus two additional inches. This allows you to overlap the edges of the insulation.
Wrap the strips of insulation around the skylight tube, overlapping the ends. Tape the strip with the aluminum duct tape.
Install insulation strips along the length of the skylight tube, and wrap the aluminum foil tape over the joints between the different strips.