We make use of the sensitivity and large sample size of the Arecibo Legacy Fast ALFA (ALFALFA) survey to investigate statistical properties of HI-selected galaxies in the local universe. This ongoing survey will eventually produce a census of over 30,000 gas-rich galaxies. The partial sample available for this work contains over 10,000 galaxies, making it twice as large as the previous generation blind HI survey, HIPASS. We have characterized the survey sensitivity and the selection function for use in the analyses presented in this dissertation, and are therefore able to make robust estimates of the characteristics of the galaxy population sampled by ALFALFA. From the available sample, we derive the HI mass function at redshift z = 0 via both the 1/Vmax and 2DSWML methods, which are in extremely close agreement with each other. These measurements are influenced by the survey design and the cosmological volume sampled, and we investigate and describe the magnitude and characteristics of the imprint of large-scale structure, survey sensitivity, and distance errors on the HI mass function. Our finding that there are more galaxies with high HI masses on the extreme end of the distribution will alter predictions for future large-scale 21 cm line surveys with such instruments as the Square Kilometer Array (SKA). The large volume and sample size of ALFALFA also allows study of the dependence of the HI mass function on galaxy environments at various scales by splitting into subsamples. This work confirms that the distribution of HI mass does change with environment and indicates that there is some threshold density beyond which the HI reservoirs of dwarf galaxies are efficiently removed, thereby flattening the HI mass function. The scale and degree of clustering for HI-selected galaxies is probed through the galaxy-galaxy two-point correlation function. Again, the large size of the ALFALFA galaxy catalog allows the sample to be split. The correlation function can thus be investigated as a function of HI mass, resolving a discrepancy from the HIPASS analysis, and as a function of optical luminosity and color. We find that HI-selected galaxies, and low HI mass galaxies in particular, are the most weakly clustered population of galaxies known to exist. For HI-selected galaxies, hydrogen mass more reliably distinguishes between environments on large scales than optical properties do, but on small scales these galaxies cluster similarly regardless of HI mass. The clustering scale of HI-selected galaxies at low redshift will help to disentangle the influence of environment on galaxy evolution, and to constrain the populations to which future large 21 cm line surveys will be sensitive. The robust measurement of the statistical properties of gas-rich galaxies at low redshifts provided in this dissertation will be used to improve simulations and models that predict the characteristics of this population of galaxies. In the case of the correlation function, we show that the clustering observed in ALFALFA can distinguish between popular models of star formation that predict the present-day distribution of gas in simulated galaxies. We suggest future projects that will further our understanding of the interplay between HI and optical properties and galaxy environment, while also providing robust observables for comparison to models.