It helps if you know the area and the road and what landmarks are around to give you a clue. Signs, poles, bridges etc. can tip you off to how high the water level is. You can pull over to the side of the road grab a stick and poke at it to get a better idea. The water will often be deeper at the edges.

Another common but unreliable tactic is to wait for someone else to try their luck and see how they manage. Some cars and trucks will do better than others. If you do take your chances aim for the middle and go slow. Still water after a storm is dangerous enough (you can't tell what's below the surface) but I'd never take chances with visibly moving water. Even shallow water moving quickly can knock you off your feet or push your car around.

If you have any doubts at all the best thing to do is to turn around and find another route. If you drive in an area long enough you get to know which areas are prone to flooding and which roads are usually safe.

People can't really tell. I would say you can be safest by assuming all visible flooding is too high, especially if you can't clearly see road markings.

A lot of people do monkey-see-monkey-do: observing other people driving through water and then trying to follow. Some people just go slowly until it feels too sketchy and then try to back up.

People inevitably get stuck.

The really big issue is when the road is lower in some spot and you don't expect it.

For example, in my city there is a road that will be perfectly clear until you hit a small section that's a low spot at an underpass. Cars driving too fast hit that section during a heavy rain and quickly get flooded/stranded.

Having driving through floods before: you don't. You either know the road before and thus know it is safe (though sometimes is washes out and you are wrong!), or you watch others and then follow the same path they did. In a very few cases there are signs that tell you (I know of a couple places where the road just crosses a stream, and the signs tell you when it is no longer safe)

You also need to know your vehicle. Some cars can wade through deeper water. Sometimes a heavy SUV will get through where a light jeep will float away. Other times the light jeep will get through and the heavy SUV gets stuck in mud.