You have to attack the village that holds the artefact with hero in the attacking army and win the attack. You also must destroy the treasury in that village. Additionally you have to have treasury required by the magnitude of the artefact in the village you attacked from. Treasury level 10 for village artefact, and level 20 for account wide and unique artefact.
Normally artefacts are heavily defended, so it is a good idea to use the combat simulator at the rally point to work out how many troops and catapults you will need to destroy the treasury and successfully steal an artefact.
HINT: Villages that have an artifact in them, cannot be destroyed to vanish from the map. That protection will lift when/if the artifact is moved or captured.