We recently identified a substantial population of galaxies at z>2 with red rest-frame optical colors. These distant red galaxies (DRGs) are efficiently selected by the simple observed color criterion J-K>2.3. In this paper we present NIR spectroscopy with Keck/NIRSPEC of six DRGs at 2.4<z<3.2. We detect continuum emission and emission lines of all observed galaxies. Equivalent widths of H alpha are 20-30 Ang, smaller than measured for LBGs and nearby LIRGs, and comparable to normal nearby galaxies. The modest equivalent widths imply that the galaxies either have a decreasing star formation rate, or that they are very dusty. Fitting both the photometry and the H alpha lines, we find continuum extinction A_V=1-2 mag, ages 1-2.5 Gyr, star formation rates 200-400 solar masses/yr, and stellar masses 1-5x10^11 solar masses for models with constant star formation rates. From [NII]/H alpha ratios we infer that the metallicities are high, 1-1.5 x Solar. For four galaxies we can determine line widths from the optical emission lines. The widths are high, ranging from 130-240 km/s, and by combining data for LBGs and DRGs we find significant correlations between linewidth and restframe U-V color, and between linewidth and stellar mass. The latter correlation has a similar slope and offset as the ``baryonic Tully-Fisher relation for nearby galaxies. The median dynamical mass is ~2x10^11 solar masses, supporting the high stellar masses inferred from the photometry. We find that the median M/L_V ~ 0.8, a factor of ~5 higher than measured for LBGs. We infer from our small sample that DRGs are dustier, more metal rich, more massive, and have higher ages than z=3 LBGs of the same rest-frame V-band luminosity. Their high M/L ratios imply that they contribute significantly to the stellar mass density at z~2.5. [ABRIDGED]
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