How does the water cycle occur in nature?
by means of evaporation, condensation and precipitation. :)
As the name water cycle indicates this is a cycle. Therefore the processes which must occur before precipitation depend upon your starting point in the cycle. I personally would stat at the point of having a body of water e.g. the sea from which evaporation must occur usually followed by transportation via wind to land which then raises the height of the clouds and causes precipitation.
Cutting of forests affects the water cycle because forests are the main part of water cycle. It is the factor which is balancing the water cycle to complete its cycle. Forests cause rain without forests, it is nearly impossible to create water cycle for the nature itself. Forests also prevents soil errosion.