Easiest way to check fans is to turn on AC and switch on the car and look. At least you will know both are working. Rest, whether they are turning auto on off without AC, that will again take 2 people and a bit of time - one revving the car from inside, the other observing the engine bay. I'd say satisfy yourself as to fans first, then move on to the other bits. As I said before, it's even possible that they maybe working but fan speed isn't adequate. That only a mechanic would know.
I'm also assuming you've checked the coolant level - both in the reservoir bottle, as well as the radiator. Also, did the car show any erratic behaviour or did you hear any boiling hissing type sounds which confirm that the car actually overheated and it wasn't just the gauge?
The reservoir bottle will also tell you if there are any excessive particles in the coolant (rust, etc.) which may inhibit its ability to maintain temperature. Rest, for example, radiator blockage, thermostat, water pump, etc. is more complicated stuff. And then finally you have coolant temperature sensors and electrical bits that may have gone haywire and can be tracked via scanner.
