Underglaze is coloured ceramic material formulated to be painted on and then covered with a transparent glaze. Because the colour sits under the glass rather than in it, the decoration stays exactly where you put it through the firing, which is what makes detailed drawing on pottery possible at all.
Why the colour stays put
A glaze becomes fluid at temperature and anything mixed into it moves with it. Underglaze contains enough refractory material that it stays where it is painted while the clear glaze melts over the top. That is the whole trick, and it is why a line drawn in underglaze survives and the same line drawn in a coloured glaze blurs.
On greenware or on bisque
Both work and they behave differently. On leather-hard or dry greenware the colour sinks in and reads softer, and the piece is then bisque fired with the decoration on it. On bisque the colour sits on the surface and reads brighter and more precise, which is why most detailed work is done at that stage. Bisque is also easier to handle without damage.
How many coats, and the usual mistake
Two to three thin coats give an even, solid colour; one coat almost always reads patchy and streaky after firing, which people mistake for a poor product. Let each coat dry before the next. Test on a tile at one, two and three coats and keep it, because the difference between coats is larger than the difference between brands.
Covering it, and where it goes wrong
Underglaze usually needs a clear glaze over it to be sealed and washable, and applying that clear is the moment work is damaged: brushing over unfired underglaze on bisque can lift the colour. Dipping is safer, and a light spray of the clear first, or a light bisque firing of the decorated piece before glazing, fixes the problem entirely.
Questions people ask about underglaze
Do I need a clear glaze over underglaze?
For functional ware, yes: the clear seals it and makes it washable. Left bare, underglaze is matt and vulnerable.
How many coats of underglaze?
Two to three thin ones. A single coat is the usual cause of patchy colour after firing.
Can underglaze go on greenware?
Yes, and it reads softer than the same colour on bisque. Bisque gives brighter, more precise results and is easier to handle.