Have Artifacts from 10 different City-States in the Museums and Wonders in your civilization.
Configure the game to start in the Industrial era, with 4 other mostly peaceful civs as opponents (Byzantium, India, Carthage, and Spain are possibilities), on a Huge map, with the maximum number of City-States (41). A low difficulty setting like Warlord is recommended. That should enable the necessary number of Artifact sites.
Turning off Barbarians is helpful, but not absolutely necessary.
At the beginning, concentrate primarily on building the Wonders that provide spots for Artifacts. Don't expand your civilization much past the 3 starting cities, but you may need a couple of additional cities to provide more room for Museums. 7-8 is probably the max number necessary, and you don't want to reset all the sites to your civilization. Do not go to war with anyone. Spawn enough units to protect Artifact sites until you can get an Archeologist to it.
Pop Culture ReferenceEdit
This achievement references the line, "That belongs in a museum," from Indiana Jones and the Last Crusade