Currency and items can be received through a variety of ways: Gambling Den, Alliance Store, Alliance Cache, Item Store, and more! Once you've earned an item, you need to use it before you get the currency or rewards.
To view your inventory, tap on the Item Store icon and then tap My Inventory
There you'll find a plethora of categories, each containing different types of items:
Each category contains:
Once you open a category, tap the Use button next to a resource to claim it. Items do not expire and can be claimed at anytime. In fact, sometimes stockpiling some resources or Hero XP items can be a great way to jump ahead in certain events!