When taking a 3 year old child's temperature for a fever, what is the most accurate way?

Rectal. The rectal method gives the most reliable, accurate reading — which is why doctors often recommend it for babies under 3 months of age, when a correct reading is crucial. However at age 3 a good quality digital thermometer, thermoscan(forehead), or ear thermometer would provide a very good evaluation of body temp and since the precise temp is not critical at this age, i would not recommend rectal.