Miners have the task of mining asteroids to get minerals, for developing better items. Equipment such as a mining suit and laser drills are some items that can be made.
The mining department is South-West of the bridge, just below Cargo. When you arrive, you'll want to grab a pickaxe and shovel. You can get equipment from the miner's closet. Some of the more notable items are a power pickaxe, three low yield explosives and a mining satchel. Next, head over to the Mining Shuttle (call it using the computer if it is not there) and send it and yourself to the mining station, which is built into an astroid. Pick up a mining hardsuit and head out into the asteroid. From there, you should start mining away at the asteroid in hopes of finding something of value. You might want to consider branch mining instead of chipping away at the edge as you will have a higher yield.