How to get an Iron or Coal Mine
The first time you go to the mine while in the map (as you said, I and C icons), if you manage to defeat all the monsters, you will be able to get the mined materials the mine has in that moment.
From that moment you can send slaves to the mines in the Village menu.
Remember that, in order to get the things you manage to achieve in your trip, you have to return to your village without dying.