The place where such wares are made by a potter is also called a pottery (plural "potteries").

Who made clay pot?

Nowadays, pottery is heated through the use of a kiln. It's widely accepted that the ancient Egyptians created the first kilns, lined with bricks made with clay and straw for insulation. They were also among the first to glaze their pottery before firing.

What do you call a person who makes clay pots?

Someone who makes pottery is usually called a "potter" in English. The place they do this is "a pottery".