Life in Classical Greece was a lot more colorful than we've been lead to believe by the weather beaten statues seen in school textbooks and on field trips to museums, and conservators have developed a wide array of techniques to determine precisely how these artifacts were once decorated. In addition to using raking light (lighting at extreme angles to reveal subtle changes in the surface of a work, which can reveal where paint was once applied) and UV light (to reveal organic compounds characteristic of older paints), infrared and X-ray spectroscopy can be used to see which wavelengths of light will be absorbed by a material, and which will be reflected. The reflected wavelength tells the researcher (approximately) which color was once applied. And let us tell you, some of these color combos are... eye catching, to say the least. Hit the source link to see for yourself.
Update: Thanks to "sir popo" (if that's his real name) for the More Coverage link!