Distance from the S minus P time
P and S waves leave the earthquake together but travel at different speeds, roughly 6 and 3.5 km per second in the upper crust. Every second of delay at the station therefore corresponds to about 8 km of distance. Multiply the S minus P time by 8 to get a quick estimate.
That rule is a simplification for nearby quakes. Wave speeds change with depth, so seismologists use travel time tables and readings from at least three stations to pin down the location.
Try it: pick "S wave (side to side)" and watch the frame and drum move while the mass stays almost still. Then drag the delay to 120 seconds and see the estimate pass 900 km.
From drum to digital
Early seismographs scratched traces on smoked paper wrapped around a turning drum. Modern instruments keep the mass centered electronically and record the force needed to do it, which gives a digital signal over a wide range of frequencies.