I also use sand. I bought a decent sized bag of colored aquarium sand and use half of it at a time for the enclosure. When it's cleaning time I remove my pet and the sticks and rinse out all the sand and junk into a big bucket. I'll then use a garden hose and fill up the bucket with water. The bug parts and poop float while the sand does not (except for little clumps of sand that I break up with the mist setting on the hose). I will do a few rounds of filling it up and dumping out the water (and junk) until the sand is clean. After decanting the majority of the water I set the bucket outside to dry which it does in time for the next cleaning.
In the housing, I'll pile up the sand to about an inch or so (3 cm) and then throw in a couple of my wife's makeup removers which are round, sturdy, and made of cotton. I soak the cotton pads and sand with a bit of water with a lab pippette (like a small turkey baster) and mist the enclosure every other day or so. The sand and cotton tend to retain a decent amount of moisture (without getting wet and soggy) and the feeder insects can't hide in it.
It's worked pretty well for me so far, but then again I'm still pretty new at this and I'm still refining my techniques.