The monsoon occurs in varying degrees, and Arizona's is marginal; not as intense as those found in other parts of the world.

In Arizona, the process starts with the hot and dry weather of May and June. Usually, the winds are from a dry westerly direction, so humidity is low and temperatures soar above 100 degrees in the
deserts. As the atmosphere warms, the jet stream retreats northward. this allows the winds to shift to a more southerly component and bring in the moisture. Most of our humid air comes from the Sea
of Cortez, but a good portion also comes from the Gulf of Mexico. Once the moist air arrives, our strong summer sun heats the moist air causing the familiar thunderstorm (cumulonimbus) clouds.

Our monsoon is the most pronounced in southern Arizona and becomes more marginal over northern Arizona. The monsoon lasts longer in the south, usually beginning around the middle of June.
In the Phoenix area, the moisture is usually here by the first or second week in July. The end of the hot and humid weather normally comes in the latter half of September state wide.

During the dry monsoon (April, May and June) we get only 6% of our normal yearly rainfall. During the wet monsoon (July, August and September) we get 32% of our normal yearly rainfall!

http://ag.arizona.edu/maricopa/garden/html/weather/monsoon.htm