Well, depends. Supernovae vary depending on their spectroscopy, and so we can deduce different types of supernovae. Most of them are core collapse, where yes, the star does collapse in on itself, the shockwave going outwards pushing all the material is what we actually see, where as the core collapse will create something like a neutron star or a black hole depending on the size of the progenitor. There is also another type of supernova caused by a white dwarf which is analogous to turning a hose on while spinning it in the air.

1.When the fusion material in a star takes more energy to fuse than it gives by fusion, the radiation pressure falls. After a certain point (depending on the mass of the star), the star will not be able to balance radiation pressure and gravitational pressure, so it collapses. If it is fairly average like our sun, it won't fall below any other outward pressure, so it would form a white dwarf. If the mass is high enough like a giant or supergiant, it passes the electron-degeneracy pressure and forms a neutron star. If it is a high-mass supermassive star, it will go past neutron degeneracy pressure and form a black hole. Depending on the state of the star at hyper/supernova (which are the only novae that form black holes), it will be spinning/not and have a charge/not. 2. Hyper novae. Don't get close ;)

John Cena