In space, the water is a very important consumable that we don’t want to waste, so the astronauts can’t have a shower.
The good thing is that, thanks to surface tension, waters sticks to your hair or your skin. So they pour some small amount of water and no-rinse soap and then they wash using towels.
In space they have a water recycling machine which allows the astronauts to reuse the water they have used! They recycle all kinds of water and it is estimated that Scott Kelly will drink 730L of recycled sweat and urine during his year in space!!
We also have a water recycling machine here at Concordia, a prototype of the one used on the ISS. Part of my job here is to test the water quality of the water from this machine.
Here is a video of astronaut Chris Hadfield showing the water recycling machine on the ISS:
at Concordia we have a similar machine which is a prototype