Once you've unlocked the Navigator Table, you can restore frescoes. Restoring frescoes unlocks trade routes to other islands.
To restore a fresco, you'll need certain items or Magic Stones. Select the fresco you want to restore and drag the required items to the fresco until the progress meter is filled.
After the required items have been dragged to the fresco, tap on the fresco to continue restoring it. Drag magic to the fresco to fill the magic meter. A timer will count down how much time you have left to refill the meter; if time runs out before the magic meter is filled, you'll have to start over again.
Once a fresco has been unlocked, clouds will disperse from its island on the Magic Archipelago map and you'll be able to trade items with the island.