The bright orange or yellow coloration of a goldfish is caused by pigment (small reflective and colored molecules) in the skin of the goldfish. These pigments are produced by specialized cells called chromatophores, and the amount of pigment produced by them is influenced by how much light the goldfish is kept in. This process is similar to how you can get a suntan. And just like if you stay indoors, your suntan will fade; if kept away from light for long periods of time, goldfish will turn pale, almost white. This is because the chromatophore cells have stopped producing pigment, and without the colored pigment in their skin, it looks pale.

There are some good resources on the exact pigment molecules and ratios that give rise to different color goldfish. For example, look for the "Pigment Types" section on this page on Goldfish History:

http://www.bristol-aquarists.org.uk/goldfish/info/info.htm