Dip a wet scrub brush into a box of baking soda so the bristles are covered in baking soda. Baking soda will remove most of the soap scum residue.
Scrub the shower door with the baking soda until the door looks and feels clean.
Rinse the baking soda down the drain with water from the showerhead.
Rub a fabric softener sheet over the shower doors to remove the white hard water residue. With the shower doors still wet, you should immediately begin to notice the hard water and scale deposits rubbing away.
Rinse the shower doors and let them dry completely. If they're not clean, continue to the next step.
Fill a spray bottle with white vinegar and spray the solution over the hard water residue. Let the vinegar sit for 10 minutes.
Scrub the hard water residue off the glass shower doors, using the scrub brush.
Rinse the shower walls and let them dry completely.