A new generation of instruments will reveal the microwave sky at high resolution. We focus on one of these, the Atacama Cosmology Telescope, which probes scales 1000 < l < 10,000, where both primary and secondary anisotropies are important. Including gravitational lensing, thermal and kinetic Sunyaev-Zeldovich (SZ) effects, and extragalactic point sources, we simulate the telescopeÕs observations of the CMB in three channels, then extract the power spectra of these components in a multifrequency analysis. We present results for various cases, differing in assumed knowledge of the contaminating point sources. We find that both radio and infrared point sources are important, but can be effectively eliminated from the power spectrum given three (or more) channels and a good understanding of their frequency dependence. However, improper treatment of the scatter in the point source frequency dependence relation may introduce a large systematic bias. Even if all thermal SZ and point source effects are eliminated, the kinetic SZ effect remains and corrupts measurements of the primordial slope and amplitude on small scales. We discuss the non-Gaussianity of the one-point probability distribution function as a way to constrain the kinetic SZ effect, and we develop a method for distinguishing this effect from the CMB in a window where they overlap. This method provides an independent constraint on the variance of the CMB in that window and is complementary to the power spectrum analysis.