We describe the PyCBC all-sky compact-object binary search pipeline, which has been used to search for gravitational waves in the first observing run of Advanced LIGO. We give a complete description of the pipeline including the steps used to identify candidate events, compute their detection statistic value and measure their statistical significance. Starting with calibrated strain data streams from the detectors, the pipeline estimates a single average noise power spectral density that is used to place a bank of template waveforms. High-amplitude noise transients are removed prior to filtering the data through this bank, and the same template bank is used for all detectors in the network. For each detector's data stream, in each template, the matched filter signal-to-noise ratio is calculated, triggers are identified in the matched filter time series and a chi-squared waveform consistency test is performed. We describe improved methods for these steps that suppress the noise background of the search and reduce the pipeline's computational cost. We describe a new method of testing that a gravitational-wave signal is observed in coincidence in a detector network, and describe the methods used to measure the false alarm rate of the search and the statistical significance of candidates events. The new algorithms used and the subsequent computational-cost reductions allow the use of a simpler pipeline topology. The pipeline can measure false alarm rate of the search to values ~ 4 orders of magnitude smaller than the pipeline used in Initial LIGO's sixth science runs at no additional computational cost. Using data from LIGO's science run, we show that the new algorithms reduce the background noise in the search, giving a ~ 30% increase in sensitive volume for binary neutron star systems.