you really have not provided enough information for someone to help you, but I'll take a stab at some basics...
Im assuming the engine is actually running hot and that you dont have a bad gauge in the dash.
Im pretty sure the fan is supposed to kick on when the AC is turned on. this is to provide airflow over the condenser.
Now onto the car running hot... Its not very complicated how the system works. as the engine heats up the thermostat opens which allows the coolant to flow through the radiator to be cooled. once the engine is warm, the thermostat should be open and the upper radiator hose should be hot as hot coolant is flowing through it going to the radiator. If not maybe the thermostat is stuck closed or backwards or the wrong temp range. The engine coolant temperature sensor monitors the temperature of the coolant and tells the ECU what the temp is. Once the temp gets to the programmed temp 220deg, the ECU turns on the low speed fan, if it gets really warm 228deg, it kicks on the high speed fan. The ECU controls the fan via the IIRC which is the black box located behind the passenger headlight.
So those are the things to check...
thermostat
coolant sensor
IIRC
fan motor
you can use a test light to test the IIRC. unplug the fan and probe the terminals to see if its telling the fan to turn on... yes the engine must be hot to do this.
The coolant temp sensor is checked during a KOEO test so that is the easiest way to see if it is working. if you do the test with the engine cold, it should say out of range and with the engine warm it shouldnt through the code.
I already mentioned how to check the thermostat, if you suspect it, go ahead and replace it. they are not that expensive.
you can test both high and low speeds of the the fan by powering it straight off the battery. one pin is ground and the other two are the high and low speeds.
the other guys around here are probably more help, but this should get you started.