You bring your water with you and you don't have a hot shower. Or, if you're seriously remote and well prepared, you filter some water from a natural source.

I suspect that there are some who stealth camp regularly and have their own cleaning methods. I have only done it a few times, and it's always been in between established campsites, so one night in the woods without a shower is not the end of the world. I try to have some wet wipes on hand for a quick sponge bath, and I clean up a little better at the first restroom I come across. I do have a water bladder that can be used as a portable shower, but I have found that situations where I might want to use the shower are also situations where I might value the extra drinking water more, so I haven't used the shower much.