If you participate even a single action in a feat, you will get a tiny rock that, when broken, has a chance of containing an artifact piece. Most of them will contain a pretty bead that isn't worth much [or if you like a piece of the newly-minted commonest artifacts, necklaces], but some will contain a piece of a rare artifact. (Top contributors are guaranteed pieces of artifacts rather than a long shot at one.)
It assembles automatically if you have all the pieces in your bags, it's not optional. So if for some reason, you want to display them split up, put one away first!