How do you mine asteriod fields?

You have to tech up to level 10 resource extraction to be able to build a remote miner.

Once you have the miners, place them on a ship, move ship to asteroid, profit.

Three notes for this.

1. Only 1 ship/base/sat can remote mine a location.
2. Theres a bug at the moment where the amount of resources obtained from mining is'nt being reported correctly. It's currently reporting double for every ship remote mining.
3. Theres another bug where multiple ships at the same location are showing positive production values (where u see maintainance) as if they were remote mining, again this isn't the true figure.

Your lord and master (below Foamy) LordHavoc

If you want to increase profit margin more, build larger mining bases. Bases usually cost less maintenance than Ships, and have more space, so you can fit in more miners.

Edit: On a sidenote, you'll need fairly large ships and portable shipyards for this.

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"He who fights with monsters should look to it that he himself does not become a monster. And when you gaze long into an abyss, the abyss gazes also into you."
-
Friedrich Nietzsche

Thanks for the info about reaching tech level 10. That's what I was missing!