Pry the skylight out of the ceiling with a pry bar. Insert the edge of the pry bar between the framing wood and the ceiling. Loosen all the edges and then pry the entire skylight out of the space.
Remove the old wood framing. If it is rotten, the wood will come away easily. You may need to use a pry bar in some spots to loosen the wood. Discard the old wood.
Measure the skylight for a new frame with a measuring tape. Get the width and length and write down your measurements.
Cut the framing wood to fit with a circular saw. Mark your cut lines on the framing wood with a pencil. Feed the wood through the saw slowly.
Screw the new frame together. Place the skylight glass in the center of the frame. Attach the wood framing pieces together with screws on each corner. Make sure the framing wood is securely holding the glass in place.
Caulk around the glass with silicone caulk in a caulking gun. Lay down a 1/4-inch bead of caulk around all the edges of the skylight glass.
Insert the skylight back into place. Lift the light back up to the ceiling and install it into the ceiling joists with a cordless screwdriver and screws.