[blam]

"This fifth or sixth century A.D. statue of the Buddha from northern India.

Wonder how they know this?

[SunkenCiv]

When they picked it up, they found "product of northern India" on the bottom.

[Gengis Khan]

Mostly they identify the source from the artistry of the Buddha statues if not anything else. Most places where Buddha statues are carved have their own distinct style. For example, Gandharan Buddha artifacts are very different from those you would find in Nepal or Tibet.