It uses photomultiplier tubes to record interactions of the cosmic rays with a good-sized chunk of atmosphere, plus detectors for the shower of particles when a cosmic ray interacts with the air. https://en.wikipedia.org/wiki/Telescope_Array_Project says it uses "a 762 km2 grid array with 1.2 km between each unit".

> The Telescope Array project ... is designed to observe air showers induced by ultra-high-energy cosmic ray using a combination of ground array and air-fluorescence techniques. ... When a cosmic ray passes through the Earth's atmosphere and triggers an air shower, the fluorescence telescopes measure the scintillation light generated as the shower passes through the gas of the atmosphere, while the array of scintillator surface detectors samples the footprint of the shower when it reaches the Earth's surface.

See also https://en.wikipedia.org/wiki/High_Resolution_Fly%27s_Eye_Co... , an earlier version.

We have other observaatories which are also pretty big, in the km-sized range.

There's IceCube, a neutrino detector observing events in a cubic kilometer of ice, at https://en.wikipedia.org/wiki/IceCube_Neutrino_Observatory .

And KM3NeT, under construction will be a neutrino detector using several cubic km of ocean, https://en.wikipedia.org/wiki/KM3NeT. It is the next generation after ANTARES, https://en.wikipedia.org/wiki/ANTARES_(telescope) .