How to Gather / Deliver Artifacts
You get a notification as soon as an explorer finds any artifact.
How to Gather Artifact
To gather it, you need to extend your territory to that location, and your carriers will then automatically pick it up and transport it to your treasury (if you have one with room).
How to Deliver Artifact
To deliver it to another village finally to get your faction reward, you need a trading post and traders who carry it to the trading post of the village.