For the DAMIC (DArk Matter In CCDs) experiment, background events from radioactive decays place the largest limit on direct detection sensitivity. Thus, characterizing and eliminating this type of background is essential to the success of the experiment. The work presented here tackles both sides of this problem using data from a previous run of DAMIC at SNOLAB. The background from radioactive contamination of detector components is characterized using simulated spectra in order to set a baseline for background rates. We also develop analysis methods to identify and reject the background from Si-32, of cosmogenic origin, using a coincidence search, which takes advantage of the spatial correlation between the two beta decays in the Si-32 - P-32 decay chain. By combining this Si-32 coincidence search with methods for physically eliminating the other dominant background components during the process of manufacture, transport, and installation, we hope to reduce background levels below 0.1 dru in the next generation of DAMIC (DAMIC-M), set to run in the Laboratoire Souterrain de Modane. Thus, this analysis is integral to achieving the high levels of sensitivity necessary to the future success of the DAMIC experiment.