Dragon mining ability is an active ability obtained by joining the dragoncrafter school. To use, open the character window with 'c', click on the Abilities tab, click on the Craft button, drag the ability to a hotkey, and activate. All active abilities, whether adventure or craft, dragon or biped, need to be dragged to a hotkey to activate.
Biped mining is a passive ability. Once you have it, from joining an appropriate school, you just need to equip a pickaxe to use it.
You can also use 'ctrl-A' to open the Abilities tab.