Purchased Item Mall items are added to your Item Mall purchase tab.
The in-game Item Mall UI can be accessed by clicking on the coins in the upper right corner of the screen or by pressing alt+b on the keyboard. Once the Item Mall is opened, left click on the "Purchases" tab on the left side. From there you can drag and drop items straight to your inventory.
Be advised that many Item Mall items cannot be traded once they are removed from the purchases tab. Be sure to check in the item's description whether or not it has trade restrictions.
You may also gift items straight from the Item Mall. To do so, left click on the desired item so that it is highlighted in red.
After that, click on the Gift button at the bottom of the tab. You will be prompted to enter a character's name. Make sure that you are on the correct server and that the name is spelled exactly as it appears or it may end up going to the wrong character.