Black holes form when mass gets crammed into such a small volume that no force can hold up the mass against gravity's pull. This happens in the interiors of massive stars as they die, and apparently in other ways as well as most galaxies contain massive black holes at their centers.

I'm not sure we know how these supermassive black holes form, although we can model it using computer simulations. Normally, when you compress gas and dust, you get stars, not black holes.