The Royal School is available for purchase at Player L14.
You must complete the Academy of Magic Quest Set in order to make your Royal School fully functional.
Completing "Orders" will cause a "Timed Quest" to appear in your Quest Side Bar - so be sure to check for them quickly, as the timer begins automatically and some have a very short duration!
NOTE: Ignoring a Timed Quest is fine, you will see the same quests repeatedly. Sometimes the objectives are very expensive or take a lot of hard to make craft items that you won't want to part with for a rune at this point. Those are the timed quests I tend to ignore.
Completing a Timed Quest gives Colored Runes as Rewards.
Hover on the different orders below to see the initial Build Requirements + Upgrade costs