Access the Roster by selecting the bottom left symbol of the home screen. The Roster tab will show you a list of your dragons. Here, you can level up, train and even pet your Dragons.
Give it a try to see their reactions!
Dragons that have a little sword symbol on their profile picture are currently in your battle team.
Select "Edit Team" to view the Dragons currently in your team and make adjustments. To make it easier to find the right Dragons for your team, tap the button with the arrows on the bottom right. It will either order your Dragons by Rarity, Power or Class.