CoGeNT employs p-type point-contact (PPC) germanium detectors to search for weakly interacting massive particles (WIMPs). By virtue of its low-energy threshold and ability to reject surface backgrounds, this type of device allows an emphasis on low-mass dark matter candidates (m sub( chi ) ~ 10 GeV /c super(2)). We report on the characteristics of the PPC detector presently taking data at the Soudan Underground Laboratory, elaborating on aspects of shielding, data acquisition, instrumental stability, data analysis, and background estimation. A detailed background model is used to investigate the low-energy excess of events previously reported and to assess the possibility of temporal modulations in the low-energy event rate. Extensive simulations of all presently known backgrounds do not provide a viable background explanation for the excess of low-energy events in the CoGeNT data or the previously observed temporal variation in the event rate. Also reported for the first time is a determination of the surface (slow pulse rise time) event contamination in the data as a function of energy. We conclude that the CoGeNT detector technology is well suited to search for the annual modulation signature expected from dark matter particle interactions in the region of WIMP mass and coupling favored by the DAMA/LIBRA results.