How do seismologists locate the epicenter of earthquakes?

By seismographs. Seismographs send seismic waves through the earth. (3 different types (s-waves, p-waves, and surface waves))

Well The difference in arrival time between the two types of seismic wave can be used to calculate the distance of the earthquake's epicenter from the seismometer, as the further away an earthquake is, the greater the lag time between the detection of the S waves relative to the P waves