Do white dwarfs give off light? If so, how are they fueling such light, and do they ever run out of light? If not, how do we find them in the night sky?
White dwarfs glow by emitting blackbody radiation.
A white dwarf is a planet sized leftover from a medium mass star. They start with a surface temperature of about 100,000 K and immediately begin to cool. As the white dwarf cools, it releases blackbody radiation into space.
As the white dwarf cools, its color moves toward the red end of the light spectrum. Eventually the star will cool enough that it will no longer be visible. At this point the star becomes a black dwarf. Astronomers do not expect to find any black dwarfs anytime soon, since it takes longer than the age of the universe for a white dwarf to cool that much.
Since white dwarf stars are very small, they can be tricky to spot, however, they can be found at the center of planetary nebulas. They are also commonly part of binary systems, such as Sirius B.