A sponge and soft liquid wash and warm water. Make sure no soap gets into the actual hot tub. Flip the cover to once side to clean side A, then flip it over to clean the other side. Most hot tub covers are very well made.
It’s always a good idea to remove your cover when adding chemicals. Over sanitizing the water can actually harm the materials of the cover. Avoid using petroleum based cleaners that can be harmful to the vinyl surface.
The inside zipper and fold should be cleaned as needed to prevent any mold or mildew from accumulating.