If your Moment battery is about to die, the watch hands will stop at 12 o'clock and the progress hand will also move to the little moon symbol without having activated Sleep Mode. You will then know it's time to exchange the battery. If you change the battery yourself, follow the directions given in the Quick Instructions precisely.
It is not necessary to exchange the battery before your Moment indicates it is time to do so. However, if you do decide to insert a new battery before the old one is completely empty, you will then need to calibrate the hands of your Moment again in order to use it. See this article for detailed instructions.