The correct order of steps for handwashing, based on authoritative health guidelines like those from the CDC, is:

1. Wet your hands with clean, running water.
2. Apply soap to cover all surfaces of your hands.
3. Scrub and lather your hands thoroughly for at least 20 seconds. This includes the front and back of your hands, between your fingers, and under your nails.
4. Rinse your hands completely with flowing water.
5. Dry your hands thoroughly with a clean towel or air dry them.

Following these steps in this order ensures the effective removal of dirt and germs to help prevent illness spread.