Modern-ish ones usually have a dirty-water-sensor; I believe it works by shining light through the water on the way out of the machine to see (roughly) how dirty it is. Clean water = cycle over, dirty water = keep going!

So if the water never gets dirty it doesn't turn off? How does it judge how dirty the dishes are to tell how dirty the water should be?

Seems fancy but nonsense.

I guess if the water is clean then it does a very quick cycle and just stops

Some dish washers have water sensors that vary the cycle times depending on how dirty they observe the return water. This why they warn you not to pre-rinse your dishes because you'll fool the system into a lighter washing which won't properly clean your dishes.

Newer models can check if the water is coming out clear and waste less resources/time.

It needs to open the inlet valve until there's enough water. This will take less time if your water pressure is higher.

It needs to heat until the desired temperature is achieved. This will take more time in colder weather.