I bought a few metres of calico, because it's a cheap, close weave natural fibre.Cut it into sheets the size of a tea towel with pinking shears (because I'm too lazy to hem anything)

When I wash produce, I lay it out to air dry on the sheets, and I throw a dry sheet into the tub or container I'm storing the veg in to continue wicking moisture.

If I'm in a rush I'll pat dry and rub dry produce that I can, but mostly it's laying it out to air dry, either on the counter or in the fridge itself before going back and putting the dry veg in a proper container.

I'll occasionally swap out the cotton in a container for a fresh dry sheet if the produce in the fridge is getting soggy. Things like lettuce and spinach for example, I'll give them a fresh dry sheet at least once a week and they'll last 2-3 weeks for me.

I tend to wash everything in a weak dilution of vinegar, in my experience that reduces moulding.

I don't have a salad spinner so when I want to spin something dry, I wash it and then put it in a mesh produce bag, go outside, and spin the bag around like a human windmill.

All the calico sheets just get thrown in the wash with all my actual tea towels and kitchen towels. If they get really gross they can be boiled to sterile clean them, or worse case scenario, composted.