Two main processes are involved in increasing the amount of water vapor in the atmosphere. These two processes are known as evaporation, and transpiration.
Evaporation is generally defined as the process by which water turns from a liquid back into a vapor or gas. This occurs due to heat energy from the sun heating up liquid water molecules in bodies of water, such as streams, rivers, lakes, and oceans, causing them to change from a liquid state to a gas, or vapor, state. It is noted that the majority of atmospheric water vapor is generated by this process (around 90%). Involved in this process, is also a process known as sublimation, when water in ice form (i.e. solid form) is converted directly to its gas form (i.e. water vapor), although this occurs rarely and only accounts for a small amount of water vapor in the atmosphere generated by evaporation.
Alternatively, transpiration, which can generally defined as water vapor given off by plants, via the same mechanism as evaporation from bodies of water, is responsible for also generating a small portion (around 10%) of water vapor in the atmosphere. During this process, water evaporates through pores, located on plants and their leaves.
Together, these process are collectively known as evapotranspiration, and provide the atmospheric water vapor necessary to drive the water cycle. Hope this helps!