You can drag the weapons into the action slots, just above where the menu icons are located at the bottom of the interface. Those action slots are set to the number keys of your keyboard.

You will need to target an enemy, you know you have them targeted when their icon and stat bars appear at the top right of the screen opposite yours. Once targeted simply using a weapon or spell or pressing 1-0 on your keyboard will cause the item to be used on the target. Holds true for all items, spells, etc.