Measure the domed section of the skylight with a tape measure, leaving out the flat mounting edge surrounding it.
Use a straightedge and a carpenter’s square to mark the location for your skylight on the roof of your shed with a marker. Choose a location without any roof trusses in the way to avoid having to cut through one to mount the skylight. Use the measurements taken to size your markings and leave room around the marked location for the mounting edge around the dome. Guide your markings with the straightedge to keep the lines straight, and use the carpenter’s square to ensure that the angles are all 90-degrees.
Cut through the sheathing of the roof with a jigsaw along the marked position. You can create a starter hole for the saw blade by drilling through the sheathing at an inside corner of the marked square with an electric drill. Remove the cut sheathing from the roof.
Place the dome skylight over the hole in the roof. Nail it in place with roofing nails through the sheathing. Use the mounting holes in the skylight for nail placement.
Cover the nails and the edge of the skylight with silicone caulking to seal the skylight in place. This prevents water from entering through the skylight into your shed.
Shingle the roof, cutting the shingles as necessary to skip over the space now occupied by the domed skylight.