The battery is located towards the lower end of the mouse in a rectangular housing, where the palm would usually rest above, along with wires connecting to its white 3-pin slot towards the opposite side of the battery location.

Remove the connector from its slot and the battery.

The new battery can now be attached in the opposite manner by connecting the 3-pin connector in its slot.

The connector pin can initally be tightly secured meaning you might require slightly more force than you expect to detach the pin. Be wary of the surrounding parts near the pin as to not damage the rest of the mouse.