The Fermi Large Area Telescope (Fermi-LAT, hereafter LAT), the primary instrument on the Fermi Gamma-ray Space Telescope (Fermi) mission, is an imaging, wide field-of-view, high-energy gamma -ray telescope, covering the energy range from 20 MeV to more than 300 GeV. During the first years of the mission, the LAT team has gained considerable insight into the in-flight performance of the instrument. Accordingly, we have updated the analysis used to reduce LAT data for public release as well as the instrument response functions (IRFs), the description of the instrument performance provided for data analysis. In this paper, we describe the effects that motivated these updates. Furthermore, we discuss how we originally derived IRFs from Monte Carlo simulations and later corrected those IRFs for discrepancies observed between flight and simulated data. We also give details of the validations performed using flight data and quantify the residual uncertainties in the IRFs. Finally, we describe techniques the LAT team has developed to propagate those uncertainties into estimates of the systematic errors on common measurements such as fluxes and spectra of astrophysical sources.