In short, it depends.
The April 10th, 2008 episode of Basic Brewing Radio is all about glass and skunking.
How Fast?
Unprotected beer will rapidly skunk. I had a keg of blonde ale in the sun one summer afternoon. The beer in the three feet of tubing spoiled in less than a minute. The small volume of skunky beer was strong enough to ruin an entire pint. It was a light beer unprotected from the sun. Dark beer in brown bottles are fairly well protected from skunking wavelengths and will spoil more slowly.
Background
Skunking is caused by a wavelength of light (350–520 nm BYO) emitted by the sun and florescent lights. Incandescent lights do not produce light in that range. The more light of these wavelengths that strikes your beer the quicker skunking reactions occur.
Colored bottles absorb & reflect wavelengths of light Wikipedia. Green & blue bottles do not absorb the whole range of skunking light making them inferior protectors. Brown bottles absorb the high frequency wavelengths and are pigmented with iron oxides. These various forms of iron absorb UV light over a wide spectrum of wavelengths.
Like bottles, beer also absorb light. Dark brown beers afford a stronger barrier protecting the liquid further inside the bottle. Light beers, like IPAs, are more susceptible to skunking.