How long does it take for a star to become a white dwarf?

The length of time taken by a star to become a white dwarf star depends on the mass of the star and may take around four hundred million more years for a star like the Sun to change to a white dwarf star. http://en.wikipedia.org/wiki/White_dwarf, has more details.

Our sun has a lifespan of about 10 billion years. During most of that time it fuses hydrogen to create an inert helium core. Then for a brief time, about 100 million years, the helium will start to fuse, creating an inert carbon-oxygen core. The sun's mass is insufficient to fuse beyond this, so it will become the white dwarf remnant of our sun while the outer layers are blown into space.

Stars somewhat heavier than our sun, around 8 - 10 solar masses, will go on to fuse carbon, creating an oxygen-neon-magnesium white dwarf after about 50 million years.

Stars less than half the mass of the sun, namely red dwarfs, will never fuse beyond hydrogen. They will not have a red giant phase, but will instead convert all their mass to helium over their lifespans. Compounded with the fact that they burn their fuel very slowly, we're talking a very long lifespan, far greater than the age of the universe. Hundreds of billions to trillions of years. But eventually they will form helium white dwarfs. Some helium white dwarfs actually exist in the universe today, but only because of mass depletion by a companion star.

White dwarfs are usually left as remnants when stars, such as our Sun, lose their outer layers of gas after their 'giant' phase.

Our Sun is about 4.5 billion years old and will become 'red giant' in about 5 billion years. After that, it's outer envelop will be blown off into space, creating planetary nebula, and the core will be left.

This core is known as white dwarf.