We report on observations of the sky region around the unidentified TeV gamma-ray source (TeV J2032+ 4130) carried out with the Whipple Observatory 10 m atmospheric Cerenkov telescope for a total of 65.5 hr between 2003 and 2005. The standard two-dimensional analysis developed by the Whipple collaboration for a stand-alone telescope reveals an excess in the field of view at a pretrial significance level of 6.1 sigma. The measured position of this excess is alpha = 20(h)32(m)27(s), delta = 41 degrees 39'17" (J2000.0). The estimated integral flux for this gamma-ray source is about 8% of the Crab Nebula flux. The data are consistent with a pointlike source. Here we present a detailed description of the standard two-dimensional analysis technique used for the analysis of data taken with the Whipple Observatory 10 m telescope and the results for the TeV J2032+ 4130 campaign. We include a short discussion of the physical mechanisms that may be responsible for the observed gamma-ray emission, based on possible association with known astrophysical objects, in particular, Cygnus OB2.