Over the past two decades, ground-based measurements of the arrival directions of TeV cosmic rays have revealed an unexpected anisotropy. Multiple detectors have recorded fluxes above all-sky averages to high statistical significance for features at large (about 180°) and small (about 5°) angular sizes. Likely sources of high-energy cosmic rays are no closer than about 100 pc, about 100,000 Larmor radii for a TeV proton in typical interstellar magnetic fields of order several microGauss.;This thesis outlines methods to search for signals in cosmic-ray arrival directions on data from the High-Altitude Water Cherenkov (HAWC) Observatory -- an extended air shower detector array in Puebla, Mexico, sensitive to gamma rays and cosmic rays at TeV energies. The detector is currently under construction, but data acquisition with the partially deployed detector started in 2013. An analysis of the cosmic-ray arrival direction distribution based on 86 billion events recorded between June 2013 and July 2014 shows anisotropy at the 10.;(-4) level on angular scales of about 10°. The HAWC cosmic-raysky map exhibits three regions of significantly enhanced cosmic-ray flux; two of these regions were first reported by the Milagro experiment. A third region coincides with an excess recently reported by the ARGO-YBJ experiment. An angular power spectrum analysis of the sky shows that all terms up to l=15 contribute significantly to the excesses. Large angular scales (>60°) are also considered, but the results are still preliminary as they are contaminated with non-sidereal signals which cancel for integer years of continuous data. An analysis of the cosmic-ray Moon shadow is shown to demonstrate the angular resolution and energy scale of the data set and to evaluate part of the analysis technique.
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