Mechanically driven fans with hydraulic clutches should have some resistance, but should turn by hand without turning the drive pulley. Make sure engine is not hot. Electric fans may turn on even with the ignition off on some cars. Some fan blades are sharp. Don't cut yourself on them.
Inspect fan blades for cracks, breaks or other damage.
Inspect cooling shrouds and ducting to make sure they are in good condition. Repair as needed. Check for electrolysis by putting positive lead of voltmeter in coolant in radiator and negative lead to good engine ground. Set voltmeter on low DC voltage setting. A blown head gasket would allow combustion gases to enter the cooling system.