There are coalmines in America that have been burning for decades, too.
What a mine looks like depends upon what is being mined, and where.
If the mineral being mined is something found in veins, the mines will follow the veins. They will be cramped, but orderly.
If the mineral is something found in small amounts, you might get a honeycomb type effect, still quite cramped, but not as orderly. Cave ins are frequent.
Minerals found in great quantities may be quarried or pit mined. You'll find great holes left over from these types of mine. This is typical of building materials like marble, granite, and limestone, but also salt and many metals are pit mined as well.
Some gemstones are "mined" by panning, because flowing water does such a good job of seperating the desirable mineral from its matrix. Gold was commonly "panned" this way in California in the 1840's, but river mining was part of the source of the worlds greatest crown jewels in history: the Persian crown jewels. The "River of Blood" from Arab legends is thought to be a particular river that was so full of ruby that the river appeared red.
Note that almost any mineral may be mined in any way, depending on the particular deposit. In parts of Brazil and Columbia, you'll find Emeralds being recovered from small pit mines.
Coober Peady, a famous opal mine in Australia, has sections in which the miners (Dwarf-like) live underground, plucking the opals from the "walls" of their homes- and some are quite normal looking (except that there aren't any windows...). Its one of the few places on Earth in which expanding your house pays for itself.
There's a salt mine in America where the tunnels are tens of yards across, and the vehicles they drive in them are the size of bulldozers...but Venice (or one of the other Mediterranean economic/military powers) "mined" salt from the sea with salt-trap ponds.
Aside: Treebore- are you a DeBeers diamond buyer?