You can use this technique on wet, leather-hard, dry, bisque fired and glazed clay. So at every stage of the clay process.
It is important, however, to match the ceramic pigment you use to your clay and firing temperature, and to dilute that pigment with screen printing medium so it becomes a usable paste.
Silkscreen motifs can be found in all sorts of shapes and styles, and if you know how to combine them creatively, maybe with your own shapes and colors, it really gets interesting. A pinch of inspiration in the examples below!