You find the Dragon Tab at the bottom of the screen

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When you press that tab, the following screen opens

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You now have three options available to you. Transform, Upgrade, and Promote.

DRAGON MOUNT PROMOTE

I hope you enjoy the game as much as I do (Happy Gaming)

Press the Dragon Mount Promote button

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A window will open and you will see this

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You now see a list of where you can get the Promote Orbs from, along with two buttons, Start and Auto Promote.
If you only have a couple of Promote Orbs I would use the Start button to add them Individually. If you have many Orb's, the Auto Promote will use your Orb's until
a) The Dragon has reached the next level
b) The Orb's have been used up.

SKILL UPGRADE

Press the Skill Upgrade Button, another window opens

You are allowed 10 spins daily.
You have 2 options, I want to cheat, this costs 50 Gold but will Guarantee 3 of the same type.

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The second Option is to pull the Bar

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This option does not cost you any Gold but will give you 3 random spins

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TRANSFORM DRAGON

Press the Transform Dragon Button and a new window will open

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This will give you all open Dragons and Mounts that you have. You can change the look of your Dragon from this window at any time.