[Abridged] We present a catalog of 68 galaxy clusters, of which 19 are new discoveries, detected via the Sunyaev-Zeldovich effect (SZ) at 148 GHz in the Atacama Cosmology Telescope (ACT) survey of 504 square degrees on the celestial equator. A subsample of 48 clusters within the 270 square degree region overlapping SDSS Stripe 82 is estimated to be 90% complete for M_500c > 4.5e14 Msun and 0.15 < z < 0.8. While matched filters are used to detect the clusters, the sample is studied further through a Profile Based Amplitude Analysis using a single filter at a fixed theta_500 = 5.9 angular scale. This new approach takes advantage of the Universal Pressure Profile (UPP) to fix the relationship between the cluster characteristic size (R_500) and the integrated Compton parameter (Y_500). The UPP scalings are found to be nearly identical to an adiabatic model, while a model incorporating non-thermal pressure better matches dynamical mass measurements and masses from the South Pole Telescope. A high signal to noise ratio subsample of 15 ACT clusters is used to obtain cosmological constraints. We first confirm that constraints from SZ data are limited by uncertainty in the scaling relation parameters rather than sample size or measurement uncertainty. We next add in seven clusters from the ACT Southern survey, including their dynamical mass measurements based on galaxy velocity dispersions. In combination with WMAP7 these data simultaneously constrain the scaling relation and cosmological parameters, yielding sigma_8 = 0.829 pm 0.024 and Omega_m = 0.292 pm 0.025. The results include marginalization over a 15% bias in dynamical mass relative to the true halo mass. In an extension to LCDM that incorporates non-zero neutrino mass density, we combine our data with WMAP7+BAO+Hubble constant measurements to constrain Sigma m_ u < 0.29 eV (95% C. L.).
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