A star doesn't just twinkle in the sky. It wages a lifelong battle against the force of gravity. The heavier the star, the stronger its gravity, and the harder it must struggle to forestall collapse. The bigger stars live fast and die young, going out in a blaze of glory. But a small star, like our Sun, might be said to die peacefully in its bed after a very long life indeed.
We describe the size of a star using our own Sun's mass, one "solar mass," as the common unit of measurement. It takes a little over .08 of a solar mass for a hydrogen-burning star to form at all. From there, we say the star is "small" if it has no more than 1.4 solar masses. This number is not arbitrary, but describes the turning point between two distinct stellar end-of-life behaviors.
All stars begin the same way; as protostars arising from collapsing nebulae. A nebula is a cloud of dust and gas, most of it hydrogen. Gravity causes this cloud to swirl and contract, forming a center mass which grows hotter and hotter as its density increases. Other masses may also form, sweeping up the nebula's outer layers; these will become planets.
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Eventually the protostar grows dense and hot enough to trigger nuclear fusion of hydrogen in its core. This process converts hydrogen into helium, producing light, heat and enough radiation pressure to stop the protostar's gravitational collapse. The protostar phase is now over, the main sequence has begun, and a new star has been born.
After about 10 billion years, a small star's core will run out of hydrogen. Nuclear reactions stop. The generation of radiation pressure ceases. Gravitational collapse happens again, increasing the density and heat of the core until temperatures are sufficient to trigger the fusion of helium into carbon. The resulting radiation pressure will cause the star's outer layers to expand to a radius as large as that of the orbit of Mercury, Venus, or even Earth. As they expand, they cool, turning red. We call a star at this stage of its life a red giant.
The process repeats when the core's supply of helium runs out: nuclear reactions stop and gravitational collapse resumes. In a small star, there will be no further nuclear reactions. Instead, stability will resume when the carbon electrons come so close together that electron degeneracy pressure occurs with enough force to balance out gravity and halt the star's further collapse.
Meanwhile, the star's outer layers expand, forming a cloud of stellar components orbiting what's left of the star's core. This cloud is a planetary nebula. The star is now a white dwarf. It will continue dimming and cooling until all of its heat energy is gone.