Supernovas are messy affairs. They don't really come in stages, but they are more complex than what most give them credit for.
The core finally burns(any reference to burning from here on out will refer to the fusion processes taking place at the heart of the star) up the last of the hydrogen after millions, perhaps billions, of years.
It's ironic that the largest stars have the shortest lifetimes. But the hydrogen is gone and the equilibrium of outward expansion due to the massive amounts of energy released by the core and the contraction of the core is upset.
The core, now composed primarily of helium "ash", begins to contract, pressure begins to build and with it, heat. The outside observer is oblivious to this process because it takes thousands, perhaps millions of years, for the energy to work it's way to the surface.
Eventually, sufficient pressure builds that the helium begins to fuse under the intense heat. This is a higher energy process than hydrogen fusion and the resultant "helium flash" blows the material above it outward at relitavistic velocites.
This will happen to our sun in a few billion years, of course Earth won't have to worry about that because she will have been swallowed by the sun's expansion around the end of the hydrogen phase.
Certain larger stars, will repeat this process until they get to iron. Iron fusion requires more energy than it generates so, finally, after many billions of years the star will cool and what will be left behind will be a mass of iron about the size of Earth but perhaps 1000 times as dense, a black dwarf. This end is assumes that the star is of course a specific mass, anything much larger and you get a sigularity, anything smaller and you get a planetary nebula.