Almeida asks: "I understand that a star collapses (due to gravity) until it becomes a Black Hole, a Neutron Star, or a white dwarf. Yet does it not undergo a supernovae and THEN become a black hole or neutron star?"
You are right: black holes and neutron stars (including pulsars) undergo supernovae explosions as they form. Young stars are hydrogen, and the nuclear reaction converts hydrogen to helium with energy left over. The left over energy is the star's radiation--heat and light. When most of the hydrogen has been converted to helium, a new nuclear reaction begins that converts the helium to carbon, with the left over energy released as radiation. This process continues converting the carbon to oxygen to silicon to iron. Nuclear fusion stops at iron. If you could slice a very old star in half, you may see serveral layers of elements.
The star now has layers of different elements. The outer layers of hydrogen, helium, carbon, and silicon are still burning around the iron core, building it up. Eventually, the massive iron core succumbs to gravity and it collapses to form a neutron core. The outer layers of the star fall in and bounce off the neutron core which creates a shock wave that blows the outer layer outward. This is the supernovae explosion.
When a white dwarf forms, however, a lot of gas is blown off (but not in a supernova explosion) to form a "planetary nebula," which looks like a giant smoke ring. The still-glowing core that is left over is a white dwarf. When it cools and no longer glows, it is a black dwarf.