You can only receive the bought skin if your Steam account's Inventory status is set to Public. In order to do this, go to your Inventory and click on the drop-down menu next to the “Trade offers” button.
Select Inventory Privacy Settings. In the panel that appears, select "Public" for Inventory.
Congratulations! The Inventory is publicly visible and you will be able to receive trade offers from us.
Remember that in accordance with the Steam’s Terms of Service, it may not be possible to exchange skins, more information can be found HERE.