With the standard rules (plains 1f(ood), 1s(hield), irrigation gives +1f, mining +1s, forest is 1f, 2s) and some fresh water in the neighbourhood,then the AI will always irrigate. If the plain has a bonus resource (grain, cow) that increases the food output to more then 3 then the AI will mine. If there is no fresh water in the neighbourhood, then the AI will mine.
If you change the output of plains in the editor or if you change the amount of food needed to maintain a unit of population then the above won't apply anymore. In general you can still say that the AI will make sure that every tile can maintain a unit of population and irrigate or mine accordingly or plant forests accordingly. It is a bit more complicated than that, but you're probably not interested in that.