The pickaxe is one of the first tools you should build, as you'll need that to get coal for your torches for when the monsters arrive.
Likewise, it's sensible to craft a sword to fend them off. Keep your most-used tools in the slots on the right of the screen for easy access.
Don't dig too deep without leaving yourself a route back up to the surface.
Most items are self-explanatory, but if you're wondering what an item is - or you've forgotten - just select it and tap the magnifying glass to identify it.