The technology they use to measure quakes is called a seismograph. Essentially, it's an instrument that measures the movement of the earth. It works by having a fixed base with a round ball. During an earthquake or other seismic events like volcano eruptions, the base moves while the ball stays still, and the motion is recorded. That record can be mathematically converted to discern the magnitude of an earthquake. Using triangulation, seismographs can also pinpoint the location of an earthquake.
Precursors to the modern style of devices came in the form of seismoscopes that merely recorded the occurrence of an earthquake. Chinese historical literature references a court astronomer called Chang Heng creating a device for identifying distant earthquakes that featured bronze dragons that dropped balls from their mouth in the event of a disturbance, and in the 1700s devices using mercury and water spillage to determine events were developed.
But seismographs that could record earth's movements weren't developed until the late 1800s, the same time seismology developed as a scientific field. The machines being produced today function using the same principles as earlier analog seismographs that recorded activity on paper, but deploy electronic sensors, amplifiers, and recording devices.
USGS releases feeds of their earthquake data online so others can use and research with it. But it also puts out its own tools -- like a map that estimates the human and economic costs and a live map that shows the most recent quakes. As of this posting there have been 44 earthquakes above a 2.5 magnitude within the last 24 hours. The most intense was a 6.7 magnitude quake off the coast of Chile.