How is MOSFET modelled in DC analysis?
There is no simple answer to this question because there are many different ways to model a MOSFET. Especially for integrated circuit design very sophisticated models like BSIM or PSP are used.

For discrete circuit design often simpler models are used, the most basic and well-known being the Shichman-Hodges model, that uses simple descriptions for the cut-off linear and saturation region.

For all these models Google should bring up a number of references.