Short of removing the pump and powering it on a bench test, you can get a good idea if the circulation pump is working or not. First, feel the pump. The pump and connecting pipes should be hot.
However, if the pump housing is a lot hotter than the pipes, it is usually bad. You can also slowly close the supply valve. When the water pressure is low, the impeller will vibrate and hum. If it doesn’t, then, it isn’t spinning and the pump is bad.