Place the mahogany door on a pair of sawhorses. Put on gloves, goggles and a face mask. Open all windows to allow for proper air ventilation. If possible, work outdoors.
Mix the urethane sealer thoroughly with a paint stirrer. When mixing sealers, you should never shake the can as this will create bubbles, which can become trapped in the finish. Stir slowly and gently until the urethane is well-mixed.
Pour a small amount of urethane directly onto the door. Keep the container close to the door, as you pour, to prevent bubbles from forming as the urethane hits the surface of the wood.
Spread the urethane slowly over the door with a foam or lamb's wool applicator. Use long, straight, even strokes. Overlap each pass with the applicator by about 1/2-inch to ensure full coverage. Coat the edges of the door by dragging the urethane from the main surface with the applicator and moving it across the edge.
Allow the urethane sealer to dry then scuff the surface of the wood with a piece of fine-grade sandpaper, around 320-grit or higher. Remove the dust with a damp cloth.
Apply at least one more coat of urethane to the door. Two coats is typically enough, but you may apply up to five or so coats if the door will see heavy use. Repeat the process for both sides of the door.