The Latin American Giant Observatory (LAGO) consists of a network of water Cherenkov detectors installed in the Andean region at various latitudes, from Sierra Negra in México 18° 59′ N to the Antarctic Peninsula 64° 14′ S 56° 38′ W and altitudes from Lima, Peru at 20 m.a.s.l. to Chacaltaya, Bolivia at 5400 m.a.s.l. The detectors of the network are built on the basis of commercial water tanks, so they have several geometries (cylindrical in general) and different methods of water purification. The LAGO network of detectors also spans a wide range of geomagnetic rigidity cut offs and atmospheric absorption depths. All these features, along with their manufacturing differences, generates different structures in the atmospheric radiation spectra measured by our detectors. One of the main scientific goals of LAGO is to measure the temporal evolution of the flow of secondary particles at ground level. The atmospheric flux produced by the interaction of cosmic rays with the atmosphere at different sites is measured to study the solar modulation of galactic cosmic rays. In the present work we describe the features of a web monitor system developed to integrate, monitor and share the data of the LAGO detectors and discuss the criteria used to estimate the signals left by the secondary particles at the detector, which are based on a novel semi-analytical method that combines simulations of the total cosmic ray spectrum and the detector's response. We also show the detector calibration method applied on three detectors of the network, including the one operated in the Machu Picchu Base (62° 05′ S 58° 28′ W) during the last Peruvian scientific campaign in Antarctica (January 2018). Finally, we review observation of a Forbush decrease measured in the detectors using this calibration technique.