Cut around the frame of the transom window with a reciprocating saw to free it from the house. Run a saw down each side of the window and along the top and bottom to loosen it from the opening. Hammer on each corner to loosen the window and carefully pull it away from the house.
Clean the rough opening thoroughly with a brush to remove any dirt and debris that may remain from the previous window. Wipe down the area with a rag to ensure it has been properly cleaned.
Measure the opening of the window for both the height and width at three separate locations. Record the smallest measurement for each to determine the rough opening for the window.
Run a bead of silicone caulk around the entire flange of the new transom window. Tip the window in place from the outside of the house and push down around the edges to adhere the silicone to the house.
Insert roofing nails all around the flange to secure it to the house. Hammer a nail in each corner along the outside and check to make sure it is level. Insert a nail every six inches all the way around the window.