Once the cover is off, lay the device on a flat surface with the screen facing downward. Use one hand to hold the device in place with the half-moon gap facing away from you [marked].

The square piece in the center of the phone is the battery. With your free hand, stick one of your fingers in the marked gap. Pull gently upwards towards you to remove.

If the battery is not coming out with this technique, use the iFixit plastic opening tool to pop it out of its holdings.