There are 7 Forerunner Artifacts scattered throughout the open world map. They can be grabbed in any order, during your playthrough or after the story missions.
The fastest way to grab them is to spawn a Wasp at a FOB and fly to them. The wasp is available for spawning at 2,600 Valor.
0:21 - Artifact 1
0:57 - Artifact 2
1:30 - Artifact 3
1:59 - Artifact 4
2:33 - Artifact 5
3:09 - Artifact 6
3:42 - Artifact 7