Minerals can be mined on foot using Ryder’s omni-tool, or by calling down mining drones from the Nomad while in a mining zone (displayed on your map, near forward stations). While exploring the Heleus Cluster in the galaxy map, you may also find anomalies containing large mineral deposits, collected with a probe.
Mineral nodes are plentiful in outdoor areas, particularly at the bottom of hills and rocky terrain, so keep a lookout.