What are some ways Mesopotamia irrigated their fields ?

Canal construction.

Explanation:

Canal construction was the primary irrigation mechanism used in ancient Mesopotamia. The entire community participated in the development of these channels. Canals were built up to twenty meters wide, and they were connected to hundreds of smaller canals. In this way, the first forms of agriculture were created. With the canal's construction, the inhabitants of ancient Mesopotamia controlled irrigation, but they also brought water to areas that did not have enough water.