When you have less than 15 spins, a spin is generated once in 10 minutes. Spins are also rewarded when you complete a task or gain a new player level. Occasionally you may also get spins as a reward floating on top of map.
If you are out of spins, you can buy more spins with gold bars. Just tap the spin button and the game will show you a pop-up for refilling your spins.