(This is getting a bit pedantic but this is HN so we like to be accurate. And I learned the word on HN so might as well pass it on.)
Several of the other answers have mentioned "triangulation" but that's not quite right--that would imply that each listening station measures an angle towards the lightning source. But they don't--instead, they collect non-directional data consisting of arrival time stamps.
I believe the word for what they're doing is "trilateration".
Edit: I originally said "multilateration" but it turns out that's not quite right, either.
From your own source: "Multilateration is a navigation technique based on the measurement of the difference in distance to two stations at known locations that broadcast signals at known times....Multilateration should not be confused with trilateration, which uses distances or absolute measurements of time-of-flight from three or more sites"
I wonder if this could be used for a lightning based positioning system independent of GPS, if the events (time + position) were transmitted on longwave like the DCF77 time signal.
Wikipedia article on sound ranging provides a nice 2d picture and example on how this works (in the context of detecting enemy artillery using an array of microphones).
Electromagnetic (link is the "participants" tab on the top). You can tell because there's a smattering of telltale RF terms in the "comments" fields (coax, ferrites, E-field antenna, etc). I imagine that lightning strikes emit a fairly broad spectrum (localization in time -> delocalization in frequency) so the detectors might not all use the same band.
I would guess they have devices that detect light and sound. When the device detects a flash, it will start a timer and wait for the sound, which ends the timer.
Then based on the speed of sound, they can estimate the distance of the strike.
With many of these devices all over the place recording the data, using math, they can pinpoint the location of where the strike was.
No sound, as it does not travel far enough and is easily disrupted by any other sounds in the area of the detector.
I think it is just waiting for input of an electro-magnetical wave, then timestamps it and sends it to the server. The server can calculate the position with just the difference in arrival time to each station, and the position of those stations.
There is a project to detect lightnings over Moscow with cheap sound-only detectors on the roofs of skyscrapers, they managed to restore ever shapes of lightings in 3D with it:
