Ultrahigh energy neutrinos are interesting messenger particles since, if detected, they can transmit exclusive information about ultrahigh energy processes in the Universe. These particles, with energies above 1016 eV, interact very rarely. Therefore, detectors that instrument several gigatons of matter are needed to discover them. The ARA detector is currently being constructed at the South Pole. It is designed to use the Askaryan effect, the emission of radio waves from neutrino-induced cascades in the South Pole ice, to detect neutrino interactions at very high energies. With antennas distributed among 37 widely separated stations in the ice, such interactions can be observed in a volume of several hundred cubic kilometers. Currently three deep ARA stations are deployed in the ice, of which two have been taking data since the beginning of 2013. In this article, the ARA detector "as built" and calibrations are described. Data reduction methods used to distinguish the rare radio signals from overwhelming backgrounds of thermal and anthropogenic origin are presented. Using data from only two stations over a short exposure time of 10 months, a neutrino flux limit of 1.5×10-6 GeV/cm2/s/sr is calculated for a particle energy of 1018 eV, which offers promise for the full ARA detector.