Vaporization through evaporation occurs only on the surface of a liquid. The other method of vaporization is boiling, which occurs throughout the liquid. Water must be 100 degrees Celsius or 212 degrees Fahrenheit.
The sun transfers energy to the molecules in the surface water via heat. The molecules begin to collide, transferring energy to each other. The molecules that have the most energy gain the energy to escape from the water, as water vapor.
Warmer temperatures can aid evaporation, as the energy in the molecules can be increased quicker. Decreases in gas pressure around a liquid can also help, as molecules tend to move from areas of higher pressure to areas of lower pressure. This is shown when water is heated and the pressure inside it increases, thus aiding evaporation from the surface.
The next step of the water cycle is condensation, when the evaporated water vapor cools and is returned to its liquid state. We know this part of the process as rain.