Gems can either be bought using $ on android or kreds when playing on kongregate. One can gain 40 (Kongregate) or 60 (android) gems for free by following the discord/youtube/play store links. The other option to get gems is from seasonal events.
Random time candy (40 gems): Get one random time candy that can be used to gain instant progress in one skill. They come in 2, 4, 8, 24 or 72 hours with varying rarity.
Vault pass (20 gems): A one time refresh of the timer on the vault. (Not worth it)
Raid tickets (15 gems): Buy three raid tickets to use to raid bosses.
Overlord mining kit (75 gems): the overlord mining kit permanently doubles the speed and ore of one miner. You need to buy one kit per miner so up to 6. They do currently not stack with the mining suits from smithing.
Infinity forge (150 gems): This changes all your forges into infinity forges, they have infinite uses and double smithing experience. (best purchase atm)
Funny hat (100 gems): Gives your fisher a funny hat that doubles the speed and experience. Each additional hat doubles both bonuses again. These can stack indefinitely. (become really good once you get multiple)