How can you tell if your fan clutch is operating correctly?

One way is upon the first cold/cool startup, you'll hear the fan roar to life, then after several seconds, 15 to 30?, it will quiet down as in freewheeling.

When operating temp is reached, and more temp is developed, you should hear the fan lock up, hear the blade noise, feel the air move. If you don't feel or hear anything, stop the engine and reach into the front of the clutch and disconnect the outer bimetal spring tab and rotate fully CW. This action should lock up the clutch. You might have to clean the spring of debris.

If you have a strobe tach, the fan blade rpm matches the pulley rpm when the clutch is locked up.

Is it possible for a new one to go bad? I just put a new one on. Should the fan freewheel when engine is cold ? Mine will turn but you can feel resistance. It is a hayden heavy duty.

Thats OK. It should loosen up when run for a short time.

There is nothing realy inside for them to go wrong....other than worn bearings that one moves the fan and can feel play.
And not all clutch fans are = get the right model for your application