OVERHEATS,COOLING FAN DOSN'T COME ON AT ALL. - 1995 Chevrolet Corsica

First thing you can do is unplug the fan motor from the harness and run wires to it (both terminals, directly to the battery...polarity isn't an issue, worst thing that can happen is that it runs backwards). Once you have determined that the fan itself is good, check voltage at the harness plug (do this with the engine hot and running at a temperature where the fan should be on)
If you find no voltage there, check the fan relay (don't remember where yours is but it's generally located with a group of relays either in the power distribution center or on a fender or on the firewall) Check the relay for operation, volts in and volts out to the harness. If you have another relay with the same prong configuration you can sometimes swap it to check.
Also check your fuses, generally the one for the fan is in the power dist center.
Most systems work the same way...the temperature sending unit on the engine sends a signal to the computer which in turn sends a ground signal to the relay which then closes and sends power to the fan motor. Therefore, it is important that your grounds are good and the sender and wiring be in good condition as well.
One note....If you are not overheating and the temp is staying low during driving, you may have a thermostat that is stuck open in which case the system will not ever turn the fan on. Since you are overheating that is not your problem but it's worth knowing. Thermostats become unreliable after a few overheats and should always be part of the repair regardless of other problems you have found and corrected. First thing you can do is unplug the fan motor from the harness and run wires to it (both terminals, directly to the battery...polarity isn't an issue, worst thing that can happen is that it runs backwards). Once you have determined that the fan itself is good, check voltage at the harness plug (do this with the engine hot and running at a temperature where the fan should be on) If you find no voltage there, check the fan relay (don't remember where yours is but it's generally located with a group of relays either in the power distribution center or on a fender or on the firewall) Check the relay for operation, volts in and volts out to the harness. If you have another relay with the same prong configuration you can sometimes swap it to check. Also check your fuses, generally the one for the fan is in the power dist center. Most systems work the same way...the temperature sending unit on the engine sends a signal to the computer which in turn sends a ground signal to the relay which then closes and sends power to the fan motor. Therefore, it is important that your grounds are good and the sender and wiring be in good condition as well. One note....If you are not overheating and the temp is staying low during driving, you may have a thermostat that is stuck open in which case the system will not ever turn the fan on. Since you are overheating that is not your problem but it's worth knowing. Thermostats become unreliable after a few overheats and should always be part of the repair regardless of other problems you have found and corrected.