You use prospecting in a cave, or you drop a minehole at an ore node and dig snaking tunnels and prospect those for metal on the floor below. When you find one, dig towards it and drop a mineshaft nearby. Probably not worth dropping a mineshaft near your first one merely because it's much harder to dig tunnels the level below.
Either way it's going to involve a bunch of random digging if you want to go past lvl 2
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