The tank system consists of a small pipe (copper) running to each tank.
In the control room there are a (electric/manual)valves, for each tank one.
There is a simple gauge next to this, or a pressure sensor.
Now you connect one tank and the compressor blows out the air for 2 seconds, then the gauge can be read.
The pressure is related to the height and the density.
Old units had a book with the densities for each tank apart, as it can be sweet/salt water or HFO, Diesel.
Also a tank table with heights and volume was needed as each tank has a different shape (Due to the position of the ship it has many columns to get the correct port/starboard and draft.
Now adays it is fully computerised.
The last one i made was for fish tanks on a trawler, as the old system was not good in seawater and they used a plate before the sensor, however the fishrests were behind this screen blocking the correct working.