how to tell water pump on car is going?

One or more of these: Coolant leak at the front-center of your car. ...
Water pump pulley is loose and making whining sounds. ...
Engine is overheating. ...
Steam coming from your radiator.

The first sign is most often seen at the "weep hole" on the pump. Often this is hard to spot and often only leaks when the engine is running. By the time the pulley develops play (wobble) the failure is in catastrophic mode.
When the coolant recover system stops working and or you notice increased coolant loss the second major cause is a failure of the seals in the water pump. The primary cause is a bad hose. It has been my experience that water pumps fail some where around 80 K miles. If the car is near that number of miles or greater it is something to consider replacing. If the engine has a timing belt often it is wise to replace the water pump when the timing belt is done. There are exceptions- some cars with a timing belt can have the water pump replaced with out removing the timing belt.

Normally it will become noisy and there will be coolant leaking from the weep hole on the water pump. 

There will either be white antifreeze residue marks or coolant coming from the water pump seep hole.

The car will become thirsty and ask for something to drink.

In general, look into the radiator.  You should see flow.

Run the heater.  If it's being fed hot water, it will keep blowing heat.

An overheating engine can have several causes, and the water pump not pumping is rare.

I saw a few water pumps decades ago that the impeller fell off the shaft, but that is rare.  There would be NO pumping in that case.

-Engine overhaul mechanic and general automotive mechanic since 1972

If there is the required amount of coolant or water in the reservoir and it's still overheating that's an indicator there's something wrong in the coolant system somewhere. To test if the pump is working squeeze the hoses with the engine running. You should feel the coolant flowing through them and they should be pretty hard to squeeze or manipulate. If you can squeeze the rubber hoses while the engine is running it's likely the pump isn't working properly.

It makes noise or it leaks or it ain't got no flow.

Usually they leak or visibly wobble.  Often the bearing seizes, the pump stops turning and the belt driving it snaps.  Very rarely (usually old car) the impeller corrodes away - the shaft still turns but doesn't pump and engine overheats.

Usually it will start leaking at its shaft seal as the failure is beginning. Water pumps operate all while the engine runs. You can look in the open radiator and see if coolant flows while being moved by the water pump. The flow will increase and decrease as the thermostat open and closes. I'm trying to understand what you meant by "going"- whether you meant, "starting to fail" or "operating normally".

Coolant is leaking out of your car, or the level keeps dropping.  Or your car overheats.

In some instances you can just hear the bearing squeal when you first start the engine but work fine as a pump. I had one last another 60,000 miles after this.

If the water pump is "going" your car will begin running hot all the time.