Simply go to your iDevice's settings>iCloud panel and login, that's it!
Your unlocked jellyfish, unlocked abilities and your discoveries will be automatically saved to your iCloud account.
Deleting and reinstalling the game, or simply installing the game on an other device with the same iCloud account you used to save the game will automatically restore your progress when the game starts.
Please note that you need an active internet connection to load your saved game from iCloud.