Use tweezers to grip the notches on the back cover, then unscrew the back cover (counter-clockwise) from the watch housing.
There is an actual tool made to remove this back cover, using the right tool may save you from scratching the back of watch with tweezers. The backcover tool can be purchased online, a local jeweler may also be willing to remove it for you.
The battery is secured to the back of the motherboard utilizing a sticky pad. Gently separate the battery from the board while making sure not to put too much stress on the board. This is best done at the location shown.