In the shop (万屋) you can buy items in exchange of DMM points, like construction materials or slots for repair (Polishing) from the seller named Mikura Bokko.
To buy an item, select the icon of the item you want to buy and click the red button that will appear underneath.
After you select the purchase button, a confirmation screen will appear asking the quantity of items you wish to purchase.
If you don't have enough DMM points purchased then you will be directed to another screen, this one will ask for a transaction to receive DMM points.
(Sorry for the quality of the last picture)