Load a caulk gun with polyurethane caulk. Pull the plunger back and drop a new tube into the gun. Pull the trigger repeatedly until the plunger comes into contact with the back of the tube. Cut the nozzle of the tube at a 45-degree angle along the bottom with a utility knife, then insert a nail or screwdriver into the nozzle to break the seal.
Climb onto the roof, using a ladder.
Place the nozzle on the corner farthest from you. Slowly squeeze the trigger and pull the caulking gun toward you, keeping it pressed against the seam where the skylight meets the roof. Use a smooth, even motion when applying the caulk. If you squeeze the trigger all the way in before you finish the seam, lift the gun off the seam and let the trigger out. Place the nozzle on the seam where you stopped, and continue caulking.
Caulk the other sides of the skylight.
Go inside and caulk the skylight from the inside. Use the same method to apply the caulk, but use clear silicone caulk.