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Ground-based arrays of imaging atmospheric Cherenkov telescopes have emerged as the most sensitive gamma-ray detectors in the energy range of about 100 GeV and above. The strengths of these arrays are a very large effective collection area on the order of 100,000 square meter, combined with excellent single photon angular and energy resolutions. The sensitivity of such detectors is limited by statistical fluctuations in the number of Cosmic Ray initiated air showers that resemble gamma-ray air showers in many ways. In this paper, we study the performance of simple event reconstruction methods when applied to simulated data of the Very Energetic Radiation Imaging Telescope Array System (VERITAS) experiment. We review methods for reconstructing the arrival direction and the energy of the primary photons, and examine means to improve on their performance. For a software threshold energy of 300 GeV (100 GeV), the methods achieve point source angular and energy resolutions of sigma[63%]= 0.1 degree (0.2 degree) and sigma[68%]= 15% (22%), respectively. The main emphasis of the paper is the discussion of gamma-hadron separation methods for the VERITAS experiment. We find that the information from several methods can be combined based on a likelihood ratio approach and the resulting algorithm achieves a gamma-hadron suppression with a quality factor that is substantially higher than that achieved with the standard methods used so far.