To help eliminate debris you could sift the soil before adding it to the container. However, this is not necessary.

If you still see a layer of sediment below the clay repeat the steps to remove the sediment.

You can repeat this process until the water is no longer forming a substantial layer.

Any cloth will do. You can use an old t-shirt or bedsheet. Be sure to use something that you don’t mind getting dirty. You can split the clay into multiple cloths to speed up the hardening process.

Be sure to hang it somewhere where you don’t mind water dripping. You could hang it from a tree or your porch. After a couple of days check the consistency of the clay. Different projects require different consistency. If you need it to be harder, let it hang longer.