In-game Shop: Gems are available in packs from the in-game Shop.  

VIP Tiers: You can get Gems by advancing through VIP Tiers.

Daily Quests: Some Daily Quests give Gem rewards. These are listed under Quests > Daily Quests.

Achievements: Gems can be obtained from completing certain achievements. You can check your Achievements in the drop-down menu, under Achievements.

Login Bonus: You can get Gems from Special Login Bonuses, such as the Monthly Login Bonus and New Player Login Bonus.  

Story Quests: Completing some Story Quests will also give you Gems. Story Quests are listed under Quests > Story Quests.