The high-frequency-peaked BL-Lacertae object \objectname{1ES 0806+524}, at redshift z=0.138, was observed in the very-high-energy (VHE) gamma-ray regime by VERITAS between November 2006 and April 2008. These data encompass the two-, and three-telescope commissioning phases, as well as observations with the full four-telescope array. \objectname{1ES 0806+524} is detected with a statistical significance of 6.3 standard deviations from 245 excess events. Little or no measurable variability on monthly time scales is found. The photon spectrum for the period November 2007 to April 2008 can be characterized by a power law with photon index $3.6 ± 1.0_{\mathrm{stat}} ± 0.3_{\mathrm{sys}}$ between $∼$300 GeV and $∼$700 GeV. The integral flux above 300 GeV is $(2.2±0.5_{\mathrm{stat}}±0.4_{\mathrm{sys}})\times10^{-12}\:\mathrm{cm}^{2}\:\mathrm{s}^{-1}$ which corresponds to 1.8% of the Crab Nebula flux. Non contemporaneous multiwavelength observations are combined with the VHE data to produce a broadband spectral energy distribution that can be reasonably described using a synchrotron-self Compton model. ; Comment: 14 pages, 4 figures, accepted to APJL