Fill a large glass jar or decanter with half way with water. Then add the ginger and let it rest for at least a couple of ours, or even overnight if you can. That way the ginger has time to permeate the water with its flavour.
Then when you are ready to serve the flavoured water, fill the dispenser with ice, about halfway full.
Stir in the sliced peaches, mint (and lemon) if you are using it.