Mining has two distinct meanings. Both involve using the Mattock, which can be received from the NPC [Pitman] Kurushack. This NPC can be found near mining areas, such as outside Moradon Castle (near the worms).

Mining fossils

Fossils can be found in Ronark Land, in the bottom left and upper right corners of the map. They are defended by Fossil Guards. The guards are easy to kill, but their attack does damage over time so you must take them out quickly. The fossils can only be attacked when you have the Mattock equipped. They drop one or two fossil items each.