What is the process that turns gas into water?

This occurs through vaporization, either by evaporation or boiling.

Water molecules in a liquid state are in dynamic equilibrium with the atmosphere: while some molecules are leaving the surface as a gas, others are leaving the gas phase to merge with the liquid. Evaporation, normally caused by heating, occurs when more energetic molecules are leaving the liquid than are returning to the liquid. At the boiling point, all of the molecules have sufficient energy to change phase to gas, and will do so if there are nucleation points. Otherwise, liquid may be superheatedpast the boiling point and spontaneously flash to steam when nucleation occurs. This can be observed by (carefully)stirring water that has been heated in a microwave to over 100°C.