What one does is contract with a supervising agency, who provides a mashgiach (a person, usually a rabbi, to supervise the kitchen and perform any halachic actions, like checking vegetables and any kashering). Kosher consumers all have at least some idea on how strict each agency is in terms of kashrut and use that knowledge to choose a restaurant, among other criteria. Any questions/differences between cooks and mashgiach should be referred to the agency as the final word.