It is amazing how the form of the clay comes out of such a messy process. Here is a very short summary of the origin of this fascinating tool from Wikipedia: Potter's wheel.
In pottery, a potter's wheel is a machine used in the shaping (known as throwing) of round ceramic ware. The wheel may also be used during the process of trimming the excess body from dried ware, and for applying incised decoration or rings of colour. Use of the potter's wheel became widespread throughout the Old World but was unknown in the Pre-Columbian New World, where pottery was handmade by methods that included coiling and beating.