The most widely-known type of exploding star, a Type II supernova
begins with a yellow star similar to our own sun, but with ten times the mass. Because of its size, a star of this type uses all of its fuel in about 35 million years (compared with about 10 billion for our sun).
Normally, the force of gravity attempting to collapse the star is offset by the pressure of heated gas undergoing fusion at the star's core. A supernova occurs when fusion is overcome by gravity...
When the star begins to run out of hydrogen, the force of gravity takes over, which in turn generates more heat. Without hydrogen to fuse, the core starts fusing helium atoms into carbon and oxygen. When the helium runs out, contraction occurs again, generating more heat, and fusing the carbon and oxygen into neon and magnesium. The process continues again, as neon and magnesium become silicon and sulfur, which in turn become iron. That's where things get a bit hairy.
The energy released fusing iron atoms is not enough to sustain a reaction. Nuclear fusion stops, and with nothing to counteract gravity, the massive iron core of the star flash-collapses in a fraction of a second...
The core collapses, then rebounds, bringing with it a shock wave. The outer contents of the star fly apart at 10,000 miles per second, performing some secondary fusion due to the immense heat of the explosion. The explosion takes out just about anything in the region at the time, appears brighter than any other object in the sky, and the collapse melds what's left into an incredibly dense, rapidly spinning collection of neutrons -- a neutron star.