In Athens, in the Archaic period, potters continued to make the clay pots with mythological scenes on them. Gradually the scenes grew and took over more of the pot, and the geometric decoration took up less and less. At the same time, a new painting technique developed. Instead of painting figures of people in outline, the Athenian potters began to paint people in silhouette: this is called black-figure, because the people are all black.
Actually black figure is done all with one type of clay. The clay found near Athens has a lot of iron in it, so it looks black when it is wet. But if you fire it in an oven where there is plenty of air getting in, the clay rusts, and turns red. This is because the iron mixes with the oxygen in the air. If you fire it in an oven with no air getting in, the iron can't mix with oxygen, and the pot stays black. So you can have either red or black pots.
So how do you get a picture? You make a pot the regular way, and let it dry a little ("leather-dry"). Then you mix a little of the wet clay with a lot of water, to make a kind of paint (called the slip), which you use to make the black part of the picture. (You can't see it now, because it is all the same color). And you let the whole thing dry.
Understanding Greek Vases: A Guide to Terms, Styles, and Techniques (Getty Museum Publications 2002) by Andrew J. Clark, Maya Elston, Mary Louise Hart