The JSNS$^{2}$ (J-PARC Sterile Neutrino Search at J-PARC Spallation Neutron Source) experiment aims to search for neutrino oscillations over a 24 m short baseline at J-PARC. The JSNS$^{2}$ inner detector is filled with 17 tons of gadolinium(Gd)-loaded liquid scintillator (LS) with an additional 31 tons of unloaded LS in the intermediate $gamma$-catcher and an optically separated outer veto volumes. A total of 120 10-inch photomultiplier tubes observe the scintillating optical photons and each analog waveform is stored with the flash analog-to-digital converters. We present details of the data acquisition, processing, and data quality monitoring system. We also present two different trigger logics which are developed for the beam and self-trigger.