It's free to play.
You can buy in game currency (V bucks) and with that acquire cosmetics (skins, emotes/dances, pick-axe designs, etc; nothing game altering).
For 10€ you can also buy the so called "Battle Pass". It includes 100 tiers: each will give you one "item" (cosmetics, XP bonus, ingame currency, etc.). You get weekly challenges (3 "hard" ones that give you one tier each, and 4 "easy" ones that give you half a tier). You get one challenge each day (for half a tier), too.
There's also an XP system which gives you options to customize certain skins.
I don't recommend buying the Pass right now, though. It's a limited event called "Season". Each season lasts 10 weeks. And there are only 4 more weeks left.
By the way: If you reach a certain tier (I think this season it was around 60), you have earned enough V bucks to buy the Battle Pass for the next season.