A black dwarf forms from a star that has exhausted all of its nuclear fuel and has cooled significantly over billions of years. Initially, a star like our Sun undergoes nuclear fusion, converting hydrogen into helium in its core. As the star ages, it eventually runs out of hydrogen and starts fusing helium into heavier elements.
After exhausting its nuclear fuel, the star can no longer support itself against gravitational collapse. For a star of moderate mass, this leads to the shedding of its outer layers, creating a planetary nebula, while the core becomes a white dwarf. A white dwarf is extremely hot and luminous, but over time, it radiates away its remaining heat into space.
It takes a very long time, typically many billions of years, for a white dwarf to cool down completely. Once it has cooled sufficiently and no longer emits significant heat or light, it becomes a black dwarf. Importantly, the universe is currently not old enough for any black dwarfs to exist yet, as it would take longer than the current age of the universe for this process to complete.