When you select a quest, a spinning gear will appear in the upper left corner. Connect the multiple gears on the right to the spinning gear to complete the quest.
The gears can be placed in any position.
There are multiple quests available, and you can proceed from any of them. You can play the quests you have cleared as many times as you like.

In this game, clockwise gear speed is represented as positive and counterclockwise gear speed as negative.