The KPNO International Spectroscopic Survey (KISS) is an ongoing wide-field objective-prism survey for extragalactic emission-line objects. Over 2200 emission-line galaxy (ELG) candidates have been cataloged to date. To study the characteristics of the survey objects, spectroscopic follow-up observations are being carried out at several telescopes. Here we present the results of the spectroscopic observations for 258 KISS ELG candidates that have been obtained using the Marcario Low Resolution Spectrograph on the 9.2 m Hobby-Eberly Telescope ( HET). We present the following data derived from the HET spectra: redshifts, reddening estimates, line equivalent widths, emission-line ratios, and galaxy activity types (e.g., AGN or star-forming). The long-slit redshifts are compared to those determined from the KISS objective-prism spectra and show good agreement. Earlier spectroscopic follow-up observations have typically verified the presence of emission lines for over 90% of the KISS ELG candidates. However, in the sample observed with the HET, only 78% of candidates are confirmed to be extragalactic emission-line sources. This is because the HET sample contains a large fraction of the faintest KISS objects, which typically have low spectral quality. A small number of objects at higher redshift (z similar to 0.3), detected by KISS from their [O III] emission rather than from Halpha emission, are identified based on their spectra.