In the Cash-Shop you can purchase mounts, serendipity potions, magical formulas and much more. To purchase Moon Stones, go into the shop and click on Moon Stones at the top of the screen. From there you can select a tariff and a payment provider.
Click on the coin symbol in the middle section of the bottom of the screen. It will open a window that offers you an overview of the item categories. If you would like to leave the shop, press ESC.
Search in the corresponding category to find the item that you are after, click on it and then click on the shopping basket. As soon as you have purchased the item, it is moved to your deposit. Click on the chest alongside the coin symbol at the bottom of the screen, select an item and click on fetch. The item can then be found in your inventory.