Native clays are dried, ground carefully between two hard stones, small pieces of stone and other impurities are sifted out, and then the fine-ground clays are soaked until they absorb as much water as possible.

The clay is then "worked" by squeezing with the hands, paddling with a wooden paddle, and generally kneaded until the right thickness or "gooiness". The clay is kept moist until ready to use. Occasionally a little sand or ground seashells are added to the clay to "temper" or make it stick together better.

When ready to use, the potter will squeeze the clay into "ropes" around to the size and shape of the pot she desires. Each successive layer is squeezed tight to the layer below, trying to get all the air out that might be trapped between the layers. After the bowl is shaped, it will be smoothed with a flat stick or polishing stone until the surfaces are hard and shiny. Sometimes designs are made in the clay with a sharp stick; other times, a carved paddle is used to "paddle" the design into the still moist clay.

The pot would be set aside in the sun for several days to dry thoroughly, then "fired" in a fireplace. Several methods were used to fire the pottery, but the one most used by the Cherokees of the period was to fill the pot with burning ground corncobs or bark burning inside would make the pot more waterproof.
From the pamphlet, "The Village at Tsa-la-gi"@ http://www.angelfire.com/ks2/tsalagilanguage/pottery.html

See also:  
Eastern Band in North Carolina - http://www.cherokee-nc.com/
Western Band in Arkansas and Missouri - http://www.westerncherokee.net/
Western Band in Oklahoma - http://www.cherokee.org/