To create a compound machine with three steps using simple machines, consider using gears, pulleys, and levers, as they offer numerous combinations. For making gears from household items, drilling holes into a wooden disk and inserting dowels can serve as teeth, mimicking DaVinci's method. Alternatively, carving teeth directly into the disk is another option, though it requires more effort. The discussion emphasizes the need for creativity and resourcefulness in utilizing simple machines for project completion. Engaging with these ideas can lead to effective solutions for building a compound machine.