The evolution of less massive stars is much the same as more massive stars, except it takes more time. A star of one solar mass—our Sun, for example—forms when a cloud of hydrogen, helium, and traces of other elements collapse under gravity. When the temperature of the core gets hot enough, fusion takes over and the star settles in for a long stable life of hydrogen burning (about ten billion years). Most of these stars (including our Sun, one day) eventually run out of hydrogen in their cores, and not being hot enough to fuse the heavier elements, slowly die, becoming red giants and blowing off their outer material as planetary nebulae.
What remains at the center is called a white dwarf, composed mostly of the carbon that forms during the red giant phase, and which slowly cools toward a cold, dark death.
So where does the Type 1 supernova come in? The answer is that the star needs help.