The origin of the extragalactic fast radio bursts (FRBs) is among the most compelling mysteries in modern astronomy. Moreover, they illuminate otherwise unseen matter and structures in the circum-galactic medium of intervening galaxies, and in the intergalactic medium. Early studies have shown that the fundamental questions posed by FRBs can only be solved with several tens to a few hundred objects with secure host galaxies. The Deep Synoptic Array (DSA) is an instrument purpose-built to discover over 100 FRB sources per year, and localize each detected burst to better than +-1.5 arcseconds. When complete, the DSA will consist of 110 4.65-m radio dishes, steerable in elevation, spread over a 2.5-km region of the Owens Valley Radio Observatory. Each dish is equipped with custom ambient-temperature receivers covering 1280-1530 MHz. We have demonstrated excellent performance, with typical system temperatures of 25 K and aperture efficiencies of 65%. A custom RF over fiber system and signal chain transports the data to a digital backend equipped with 37 Smart Network ADC Processor FPGA boards for digitization and packetization, and 24 GPU-equipped servers for correlation, beamforming, and FRB searching. Monitor and control requirements are served by a novel system based on a distributed key-value store. The 11.3 deg2 field of view is coherently searched in real time for FRBs using a Tee-shaped core of 95 antennas, and the full array is used for rapid localization. Accurate FRB positions will be delivered to the community via a VOEvent service within 60 seconds of detection, and all FRB data products will be hosted on a publicly accessible web server. At present, the DSA is in a construction and early science phase, with 25 antennas being used to shake down the system while the full array is built. The DSA is funded by the National Science Foundation under grant AST-1836018.