What process returns water to earth's atmosphere?

It is all part of the water cycle. It does not matter when it starts since nobody can really define it. However, water cycles involves 2 (or 3, for some) processes most of the time. Evaporation and transpiration (water is lost to surrounding) changes the water to water vapour, then rises up to the earth's atmosphere. It then condenses to form clouds, before it falls as rain, snow or hail as a process of precipitation. These waters would then sip into the ground as groundwater or run into the water bodies by surface runoff before the whole cycle repeats itself.