How did farmers in the fertile crescent bring more water to their farms

This process is called irrigation, and it is claimed that irrigation was developed there (and it was also developed in China independently around the same time).

In Mesopotamia people used an irrigation of canals: they had built a number of small channels that diverted the water from the rivers towards the fields.

In Egypt, the water of flooding was stored and re-introduced at a later time to prolong the "flooding" period.

(Egypt and Mesopotamia were two regions in the Fertile Crescent)