Earn gems by purchase them in-app purchase is the fastest way, but you can also get free gems as you progress through the game. The trophy icon shows you all achievements, and you will have the ability to gather gem rewards from the ones that you have actually completed. Also don't forget to watch those video ads for some extra gym bonuses.

Go to your Powers menu, which is inside the icon that appears like falling gold, to get some powers and gold rain for percentages of gems. Or go to the store, barracks, or jail. The store includes irreversible bonuses, the jail unlocks new heroes for gems. Well if you know better cheats or other hints, them submit them... have fun!