To release an animal back into the wild it needs to be in your inventory. To return an animal in your zoo to your inventory, simply click on the button in the ring menu:
Once it's safely back in your inventory, click on the animal in your shop or inventory. You'll see a larger image of it on the right side, and below it, a blue button with some money on it:
Clicking this will open a window where you can choose to sell or release the animal:
Make sure that you have selected "Release" and adjust how many of that type of animal you would like to release in the bottom left-hand corner. Simply tap "Okay" to confirm. You will receive experience points for releasing the animal; the more valuable the animal is, the more experience points you will receive.