Same way like other pharaonic infastructure projects PRC has done, doing, and planning to do. Gaddhafi's Libya made the vastest irrigation project in the human history. Why PRC nowdays can't do something as colossal and even bigger? They managed to build 30.000 km of electrified high speed rail in 10 years. We shall not try to "translate" Chinese reality with Western style economics and politics. Even now, with that mixed and somehow confusing model, Chinese governance is still pro-people and not cost accounting if a project benefits all. PRC is far more leftist than the leftier western democracy and we have to add that to the equation.
Anyway all this thing discussed is just a speculation
And yet that great Libyan water project only supplies the water needs of 4 million people.
My issue is that even if you add all the societal benefits, I doubt the cost-benefit equation of sending water to Xinjiang works.
Even sending water to Qinghai, Gansu and Inner Mongolia would make more sense - rather than sending it to Xinjiang.
Suppose the water was diverted to Qinghai, and then connected up with the Yellow River.
The additional water passes through Lanzhou (Gansu), Yinchuan (Ningxia) and the Inner Mongolia cities, before connecting to the North China Plain.
Ningxia and Inner Mongolia are sparsely populated, so could support more population and agriculture.
There's also the Ordos Desert which could be irrigated if you really want to transform a desert.
These places are adjacent to the densely populated Chinese core, so transport costs aren't a significant issue.
A renewed Yellow River could also serve as a transport artery deep into the interior.
It would serve a similar function as the Changjiang River or the Mississippi River.