Mining always involves a mining ship that can harvest the raw resources that form the building blocks of the various economies in the Universe.

There are two main types of resource:

Bulk Resources

Bulk resources are solids that are harvested from asteroids.  This requires that asteroids with resources are found, broken down into smaller chunks, and harvested.

To break an asteroid down to smaller pieces, a weapon of some sort is necessary.  While any weapon will do, mining lasers are particularly efficient at breaking down asteroids.

To harvest the broken-down asteroids, a mining ship needs Surface Miner drones to pick them up, and Bulk storage to store them.

Player-assisted Mining

You can assist in mining particular bulk resources by:

Automatic Mining

It is also possible to completely automate this process by simply ordering the crew of a mining ship that you own to mine a particular resource in a particular area.  Please note, however, that it is possible that the mining ship will be unable to find any of the resource you ordered them to mine.

Liquid Resources

Liquid resources are non-solids that are simply harvested from an environment that contains those resources.  These non-solids are then refined by the harvesting ship and are stored and transported in liquid form.

To harvest liquid resources, a mining ship needs Scoop Collector drones to harvest them, and Liquid storage.

Since liquid mining does not involve anything that can be broken down and tagged, player-assisted mining does not apply to mining liquid resources.