Special thanks to Picho, info taken from Nodiatis forum.

To mine, you first need a Mining Hammer.
These are sold in T2 (Stronhad) for 1200 gold. Once you have that in your inventory you need to go find an area in which you can mine. I believe that anywhere with a mountain in the background during combat will work, need someone to verify this, though.
Anyway. Once you are in a suitable location, you must successfully defeat a monster - anything will do, even greys. After you beat it and exit looting, the mining icon will appear at the bottom of the screen. Click it to enter the mining mini-game. Put your mouse over the giant rock that appears and hit spacebar to throw a hammer at it. It will break up, and you have to throw hammers at the pieces that appear.
Lather, rinse, repeat, and you will get either an ore or a worthless rock. I have only had rocks appear while mining at Troll Bridge, though.

If you have a Stone Saw (sold in T4, Atlimus) you can turn the ore into geodes.
Otherwise you need sticks to turn the ore into ingots.

Mining Mining Level Required to Process Ignots
Citrine Ore Citrine Geode 0 Citrine Ingots
Liliac Ore Liliac Geode 3 Liliac Ingots
Coal Ore Coal Geode 6 Coal Ingots
Quartz Ore Quartz Geode 10 Quartz Ingots
Jonquil Ore Jonquil Geode 13 Jonquil Ingots
Capri Ore Capri Geode 17 Capri Ingots
Spotted Tabac Ore Spotted Tabac Geode 20 Spotted Tabac Ingots
Apetite Ore Apetite Geode 24 Apetite Ingots
Amethyst Ore Amethyst Geode 27 Amethyst Ingots
Amazonite Ore Amazonite Geode 30 Amazonite Ingots
Aquamarine Ore Aquamarine Geode Aquamarine Ingots
Coral Ore Coral Geode Coral Ingots
Lace Agate Ore Lace Agate Geode Lace Agate Ingots
Emerald Ore Emerald Geode Emerald Ingots
Firestone Ore Firestone Geode Firestone Ingots
Boreale Ore BGeodeale Geode BIngotsale Ingots
Volcano Ore Volcano Geode Volcano Ingots
Calcite Hive Ore Calcite Hive Geode Calcite Hive Ingots
Onyx Ore Onyx Geode Onyx Ingots
Chrysolite Ore Chrysolite Geode Chrysolite Ingots
Crystal Ore Crystal Geode Crystal Ingots
Erinite Ore Erinite Geode Erinite Ingots
Aquadepths Ore Aquadepths Geode Aquadepths Ingots
Diamond Ore Diamond Geode Diamond Ingots
Aurum Ore Aurum Geode Aurum Ingots
Nepherite Ore Nepherite Geode Nepherite Ingots
Labradorite Ore Labradorite Geode Labradorite Ingots
Suzulite Ore Suzulite Geode Suzulite Ingots
Temorite Ore Temorite Geode Temorite Ingots
Livmalign Ore Livmalign Geode Livmalign Ingots
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