This thesis is a study of the very high energy gamma-ray emission from the hard spectrum blazar 1ES 1218+304. The data were collected during the 2008/09 observing season by the VERITAS observatory, an array of four atmospheric Cherenkov telescopes in Southern Arizona. This work describes the development of a set of analysis tools suitable for the extraction of the energy spectra of astrophysical objects. Initially, the tools are applied to the Crab nebula data to optimize and calibrate the analysis. Afterwards, the analysis is applied to the high energy observations of the blazar 1ES 1218+304. We report an intense, day-scale flare observed on January 30, 2009. This marks the first detection of variability in gamma-ray emission from 1ES 1218+304. I also investigate the possibility of detecting a spectral feature in the observed energy spectra of blazar due to extragalactic background light. I demonstrate the presence of a spectral cut-off in the simulated multi-TeV energy spectra of blazars at around 1 TeV. This novel technique has a strong potential to discover the first observable signature of absorption of very high-energy photons due to the extragalactic background light.