You can get a mining tool (pickaxe) from the marketplace (Royal Emporium). You can see the location of the Royal Emporium by opening your map (press M or TAB). The mining tool you’re looking for is “crude pickaxe” and has no level restrictions (can be used from the first level). You will need some gold to buy it, prices fluctuate, usually around 50 gold, but it may go to 100 gold sometimes depending on supply and demand.
Another way to get a pick-axe is at the engineering bench (see on map). But the items required to build it cost more than buying the actual pickaxe, so if you’re just starting out, it’s easier to get some gold and buy the pick-axe.
How to equip the mining tool (crude pickaxe)?
To equip the mining tool you need to go to your stash in the tavern, upstairs. Open your stash and right click the tool to equip it, or simply drag it.
If your pick-axe is not in your stash, check if you collected it from the Royal Emporium (marketplace) first. After you purchase an item it stays in the Emporium until you click the Collect button, which sends it to your stash.