The little vent they open with the screwdriver ("spit valve" it's sometimes called) will tell when the tank is filled to the proper capacity, with appropriate headspace, by starting to dribble out liquid propane rather than just a bit of gas.
For DOT cylinders, which I believe is what you're talking about, there are three basic ways to tell when they're full. One is using the vent. Another is using a scale, set to the tank tare weight plus the weight of propane plus the weight of the filler adapter. A third is to rely on the OPD valve which has a float mechanism to shut of the flow when it reaches a certain level, sort of like a toilet tank valve. I'm not an expert, but I'm under the impression that relying solely on the OPD valve is not generally permitted; it's more of a safety backup.
For built-in tanks, the same basic ideas apply except it's obviously not practical to fill by weight.