Mild soap and a soft brush are all you need.
That’s it. Nothing fancy. You don’t need the pool-store special cleaner or a pressure washer.
Spread the cover flat on the lawn (or clean it while it’s still on the pool, whichever is easier). Mix a small amount of dish soap or mild laundry detergent with water. Use a soft-bristle brush or a sponge—no scrub pads that can tear the plastic. Gently scrub the gunk off, then rinse thoroughly with a garden hose.
Why not the heavy stuff? Harsh chemicals (bleach, ammonia) will degrade the material. High-pressure sprayers can punch holes in the bubble film. Abrasive tools will scratch the surface, making it harder to clean next time.
One extra thing: rinse off all soap residue. Soap left on the cover can foam up when it hits the pool water. But that’s easy to avoid.
Your cover will stay clear and last longer if you clean it this way once or twice a season.