We see the star brighten quickly, and fade over time. There are two types of supernovae. If the gas coming from the normal star comes at just the right rate, it can pile up more efficiently than in a regular nova. When it finally fuses, the release of energy can be much larger than a nova, and can actually blow the white dwarf apart. To be honest, no one is completely sure how this works.
Some models involve two white dwarfs coalescing.
The other type of supernova involves a star with a mass greater than about 8 times the Sun's. There are a great many details involved, so I'll be brief. The star fuses hydrogen into helium in the core. When hydrogen runs out, the helium fuses into carbon, the carbon into oxygen, and so on, until the core is mostly iron. Unlike the previous elements, iron does not release energy when it fuses.