Humidity is measured with an instrument called a sling psychrometer.
This instrument consists of two thermometers. One thermometer measures the air temperature while the other one measures something called the wet-bulb temperature (a thermometer with a cloth wick on the end).
After the wick is dipped in water, the sling psychrometer is whirled around using a handle. Water evaporates from the wick on the wet-bulb thermometer and cools the thermometer. You can then determine the humidity by calculating the difference between the two temperatures. Pretty high-tech, eh?