What instrument is used to measure relative humidity and how does it work?

The measurement of humidity may be done directly by a hygrometer.

But the usual instrument is called a psychrometer, which uses two thermometers to obtain temperatures that indicate the relative humidity.

A psychrometer is an instrument that uses the difference in readings between two thermometers, one having a wet bulb and the other having a dry bulb, to measure the moisture content or relative humidity of air. When air is saturated, the bulbs have the same temperature. When it is less than saturated, the moisture around the wet bulb evaporates, cooling the wet bulb until it is cooled to the temperature where the concentration of water vapor in the air would saturate air at that temperature.

psychrometer

Relative humidity is a measure of water vapor in the air compared with the maximum amount of water vapor the air can hold at that temperature. It can be measured by using a variety of instruments, such as a thin polymer film, a psychrometer, a dew cell, and a hair hygrometer.
sling psycrhometer
A hygrometer or a psychrometer will measure relative humidity.
A hygrometer.
psychrometer
Thermo-hygrograph. It uses two thermometers, one gives dry temperature is is hung in the air, while the second one is dipped in water with the help of a wick. As the evaporation of water depends on the relative humidity in the air, when there is a big difference in dry and wet temperatures it means that humidity is low and vice versa. The exact humidity is found out with the help of a table Relative humidity can be measured by a psychrometer .