We study the prospects for extracting detailed statistical properties of the neutral hydrogen distribution during the era of reionization using the brightness temperature fluctuations from redshifted 21 cm line emission. Detection of this signal is complicated by contamination from foreground sources such as diffuse Galactic synchrotron and free-free emission at low radio frequencies, extragalactic free-free emission from ionized regions, and radio point sources. We model these foregrounds to determine the extent to which 21 cm fluctuations can be detected with upcoming experiments. We find that not only the level of correlation from one frequency to another but also the functional form of the foreground correlations has a substantial impact on foreground removal. We calculate how well the angular power spectra of the 21 cm fluctuations can be determined. We also show that the large-scale bias of the neutral hydrogen gas distribution with respect to the density field can be determined with high precision and used to distinguish between different reionization histories.