The first dusty white dwarf, G29-38, was discovered in 1987 by Ben Zuckerman and Eric Becklin in a search for brown dwarfs areound white dwarfs. Since the launch of Spitzer, almost 20 WD disks are known, shown below ordered by year of discovery (click on the image to zoom in to full detail):
One thing you will notice is that most of these disks are not much bigger than the extent of Saturn's outermost rings, and that to date there is actually a fair bit of variability in terms of the location of the inner and outer edges of these disks. It is not precisely known how these disks form and how long they last. All of these disks, however, are directly accreting onto the surface of the white dwarfs, which shows up in the spectra of the WDs themselves as narrow absorption lines caused by elements such as Ca, Mg, and Fe. If enough elements are detected, you can learn the atomic abundance of the dust accreting onto the WD, giving you an unparalleled view of the composition of the dust in these disks. Most of the abundances done to date show that the dust is very similar to the bulk composition of the Earth and asteroids.