We present a cosmic shear study from the Deep Lens Survey (DLS), a deep BVRz multi-band imaging survey of five 4 sq. degree fields with two National Optical Astronomy Observatory (NOAO) 4-meter telescopes at Kitt Peak and Cerro Tololo. For both telescopes, the change of the point-spread-function (PSF) shape across the focal plane is complicated, and the exposure-to-exposure variation of this position-dependent PSF change is significant. We overcome this challenge by modeling the PSF separately for individual exposures and CCDs with principal component analysis (PCA). We find that stacking these PSFs reproduces the final PSF pattern on the mosaic image with high fidelity, and the method successfully separates PSF-induced systematics from gravitational lensing effects. We calibrate our shears and estimate the errors, utilizing an image simulator, which generates sheared ground-based galaxy images from deep Hubble Space Telescope archival data with a realistic atmospheric turbulence model. For cosmological parameter constraints, we marginalize over shear calibration error, photometric redshift uncertainty, and the Hubble constant. We use cosmology-dependent covariances for the Markov Chain Monte Carlo analysis and find that the role of this varying covariance is critical in our parameter estimation. Our current non-tomographic analysis alone constrains the Omega_M-sigma_8 likelihood contour tightly, providing a joint constraint of Omega_M=0.262+-0.051 and sigma_8=0.868+-0.071. We expect that a future DLS weak-lensing tomographic study will further tighten these constraints because explicit treatment of the redshift dependence of cosmic shear more efficiently breaks the Omega_M-sigma_8 degeneracy. Combining the current results with the Wilkinson Microwave Anisotropy Probe 7-year (WMAP7) likelihood data, we obtain Omega_M=0.278+-0.018 and sigma_8=0.815+-0.020.
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