To level up your dragons, you must feed them and, of course, train them! In order to do this, you can select a dragon by tapping on them on your Berk or in the Hangar. On the bottom left-hand side of the screen, next to the banner with their information, you will see the button to FEED or TRAIN (Fish icon for feed, Wood icon for train). The top of the button will also show the required amount of the Fish/Wood/Iron needed, so be sure to have your storages well stocked!

 

You will need to feed your dragon 3 times per level (4 times after Level 52 Titan). Every 2 levels, your dragon will need to be trained at the Academy instead of being fed. This process takes time, during which your dragon cannot be used.

 

As you level up your dragon, their skills and abilities increase but so do the resource costs for feeding and training them!