Scientists use a rain gauge. The rain gauges have wide openings at the top for rainfall. The rain falls and is funneled into a narrow tube, one-tenth the diameter of the top of the gauge. Precise measuring to the one-hundredth (1/100 or .01) of an inch is possible. When less than .01 inch of rain falls, that amount is known as a "trace" of rain.

By the way, when you talk about precipitation most people are probably mostly thinking of rainfall but it also includes snow, hail, and other forms of water falling to the ground. It is measured in units over a given time (inches per 24 hrs or mm/day, etc.)

Here is a good web site that explains more:
precipitation