There isn't much to a sponge, in the way of complexity. They have been described as a collection of specialized cells into a structure -- it is a multicellular animal, but the most primitive. Some modern sponges don't have skeletal material, but fossil sponges can have either calcite or silica spicules of varied shapes. This isn't like a solid skeleton, exactly, but often there is enough holding the tissue of the sponge together after death and burial, so that we see a kind of combination fossil, involving impression of soft tissue, along with the tiny spicules embedded within it.
This photograph of a modern sponge shows a familiar branching form, which is soft to the touch and squeeze:
This sponge wouldn't fossilize too well. Sponges of ancient Paleozoic oceans though, had spicules of calcite or silica, and we do find them as fossils, common in some limestone beds. This fossil sponge has star-shaped calcite spicules:
The shape of this particular sponge is rather disc-like, or cup-like, and lumpy, but remember that we have to factor in that compaction has distorted the shape from the original form of the animal. In life, this sponge would have been bowl-shaped, but more full-bodied. If we zoom in, we see the star-shaped calcite spicules characteristic of this group (look on the right side of the image):
A sponge from the Paleozoic Era that had a characteristic shape and texture is Hydnoceras , a glass sponge (silica spicules):
Hydnoceras has the unique cross-hatched pattern seen in modern glass sponges, and also has a distinctive "knobby" appearance.