I use gravity for a simple cleaning.
I dig a hole in the ground, add dirt and water and stir. The bigger sediments sink to the bottom and the organics skim on the top. The actual clay stays suspended. I scoop out the sediments and the organics until I can't feel anything in the hole and then I stir again so I can get the smaller sediments when they fall out. After that you let the water drain out of the hole and your left with clay with the consistency of sticky slightly wet whipped cream. You scoop it out and keep it. Make sure not to scoop up the layer of sediments you missed. Leave a small layer of the clay behind to make sure of that. After that I take my clay I let it dry out a bit and then I let all the stuff in the hole dry out so I can scrape it out and start the process again.
I squish it between my fingers and still feel a bit of tiny sediment so I dry it out and put it back in the hole.