The ARIANNA experiment will observe high-energy cosmogenic neutrino signatures via a large array of autonomous radio listening stations dispersed on the Ross Ice Shelf in Antarctica. Each station in the projected array of 900 stations will contain RF antennas, amplifiers, digitization, real-time triggering circuitry, a CPU with solid-state data storage, and redundant remote communications paths. Power is provided by both sun and wind. Two prototype stations have been installed, with a hexagonal array of seven stations, with each positioned 1 km apart, due for deployment over the next two seasons. The station's core data acquisition system includes four channels of analog sampling circuits that operate at 2 GHz and achieve over 11 bits of dynamic range. These circuits sample continuously over a 128-sample circular analog storage array. The circuits use a phase-locked loop to generate the 2 GHz internal sample clocking from a ~ 30 MHz external clock. Unlike most previous such designs, the high-speed sample clocking is completely synchronous and has very high timing stability, with about 1 ppm RMS jitter. The sampling circuits include the ability to produce a real-time trigger based on pattern-matching of the incoming waveform. Up to 72 patterns can be searched for in parallel, and each pattern looks at 8 consecutive samples, requiring that any or all of the samples be above a high threshold, below a separate low threshold, in-between the two thresholds, or a “don't care” condition. Each station also includes computing and solid-state event storage, environmental monitoring of voltage and power consumption, wind and temperature conditions, and both long-distance wireless to McMurdo Station and Iridium satellite communications. For the 2011-2012 austral season, about 1.4 million events were acquired between the second station's installation on December 21, 2011 and March 15, 2012.