The moon Tethys, as seen by the Cassini probe.
Tethys, a moon of Saturn, is known to have a density of 0.98 g/cm³, meaning the moon is almost 100% porous water-ice. It has a diameter of 660 miles and surface features include plains, impact craters, chasmata and troughs.
Terraforming Tethys would involve adding an initial atmosphere of strong greenhouse gases, and through electrolysis of the water, oxygen could be created; Nitrogen can be exported from Titan. As soon as the rest of the ice melts, it would create an ocean which would entirely cover the moon, down to it's core. Much like on Enceladus, to live on the surface, Artificial Continents that float over the water, would need to be created and covered with plant and animal life.
This far from the Sun, orbiting mirrors would be impractical (and the materials to make them, silicates and metals, are not abundant here). Thus, a ring, or 'cloud', of advanced fusion satellites would be needed to provide the water world with heat. This would have to be done in advance, as the previously mentioned greenhouse gases would just freeze on the surface of the body.
Atmospheric esape would also be an issue due to the low gravity (barely 1.5% Earth's),; Tethys might therefore be paraterraformed shortly after receiving its atmosphere. This would involve building a large, transparent "bubble" over the moon, which would be held up by air pressure and intermittent collumns.
A thick enough atmosphere, along with the protection of Saturn's magnetosphere, would likely be enough to keep colonists safe from damaging cosmic rays and the solar wind. If not, the colonies can simply move a few meters beneath the waves.
See also: Tethys Simulation
