Measure the dimensions of the attic door with the tape measure.
Remove all molding that surrounds the door. Gently use a claw hammer or small crow bar, and avoid damaging the attic door or surrounding ceiling.
Construct a decorative grid of molding across the entire ceiling, where each "box" is exactly the same size as the molding surrounding the attic door. The molding can be plain strips of wood or elegantly shaped - the choice is yours. Dado rail (also known as "chair rail") or bed molding may look the best on the ceiling, but discuss your plans with your local hardware store when choosing the molding.
Begin building the grid by first framing the attic door with the molding. Affix the molding to the ceiling with the nails. The molding must completely disguise the gap between the door and the ceiling, but you should ensure that the attic door has clearance through the molding. Then install the molding outwards across the ceiling, making each "box" look identical to the "box" surrounding the attic door.
Remove any hardware (knobs, rope handles, etc) from the attic door. Paint any hardware that cannot be removed (i.e. hinges) to blend the hardware into the ceiling color. If the attic door is simply a panel that is pushed up and out of the way, you are finished. If the door must be pulled down, move on to the next step.
Remove the "guts" of a smoke detector. Make as much empty space inside the detector as possible, but do not damage any mechanisms that hold the lid shut.
Mount the empty smoke detector on the attic door, centered on the side opposite to the hinges.
Drill an eye-bolt through the inside of the detector and into the attic door. Ensure that it is tight and seated deeply enough that the lid of the detector can still close.
Tie the rope to the eye-bolt and coil the rope inside the detector. Close the lid to hide the rope.
When you need to drop the attic door, open the detector and pull down on the rope.