The Nosefish shower was designed by Howard Cohen in 2006 and has been built and used by countless burners since then. It is simply a PVC shower frame on a short wooden platform built at a slight angle and with a hole in the lowest part, so the shower water can be collected.
We used to filter the gray water, treat it with bleach and sprinkle it on the Playa, but this is now forbidden. Recommended ways of dealing with gray water include taking it home, evaporating it, or hiring a service to haul it away.
All the construction details are at:
The first Nosefish Shower circa 2006