Use the point of a spudger to pry up the battery's press connector.

When you disconnect connectors like these, be careful not to dislodge the small surface-mounted components surrounding the socket.

To re-attach press connectors, carefully align and press down on one side until it clicks into place, then repeat on the other side. Don't press down on the middle. If the connector is misaligned, the pins can bend, causing permanent damage.