The Lunacraft controls include two "swipe areas" and several small buttons, plus a "quick bar" used to select items in your inventory. The left half of the screen is used for movement, while the right half is used for looking around. (There are large circular icons for these actions, but in fact you can touch nearly anywhere on the screen to move or turn). Two small buttons on the right side are for using the selected item and using the jetpack. A small icon in the upper-right lets you change options and save/exit.
To mine blocks, you must select the drill, aim at the block you wish to mine, and hold the action button. Cracks will appear in the block, and after a second or two, a smaller block will pop out as the larger block disintegrates. You must walk over the smaller block to collect it, and it will appear in your lower dock (quick inventory).
A little double-chevron button lets you expand the lower dock to show your full inventory and the Assembler.