Aquatic mosses can be considered to be the easiest aquatic plants to grow in the tank. In general, if you can keep Java Fern alive, you should have no problem keeping Java Moss and most of the aquatic moss.
Tank Size
Any tank size will do. You can grow it in a nano cube tank of 15cm X 15cm or a 6ft tank. However, to really appreciate the beauty of the fronds of the moss
Water
you can use water that comes right out of my tap.
Lightings
This is the part where the moss excel in. It can grow in different light levels. If the light level is just enough for you can see the moss in the tank, it is sufficient to support moss growth, though very slowly. As a general rule, the higher the light, the faster the moss grow.
Fertilizer
With or without additional fertilizer, the moss will still grow.
CO2
With or without additional CO2, the moss will still grow.
Water Temperature
In general, most of the mosses grows better in a slightly cooler water temperature of less than 28°C. The exception is Java Moss, which grows well even in higher temperature exceeding 30°C.
Aquascaping
The beauty of the moss is best presented when it is grown attached to something, example, rocks, driftwood, or as a background moss wall. Though it will still grow even if you just dump it into a container, you can't really see the beauty of it
In summary
There isn't a 'right' way to grow aquatic moss. You can invest in a high tech setup with auto CO2 controller, daily fertilization, and an MH lighting system.