Be sure to not puncture the battery. It may explode or catch fire if it is mistreated. Proceed with caution. Especially if your battery is puffy!

Carefully slide the batter toward you (Away from the motherboard, imagine you are in the perspective of the image)

Do not lift the battery directly. You might harm the wire going over the battery. Make sure you slide it out from under the wire before you completely remove it from the housing.