We investigate the gas content and baryonic Tully-Fisher relationship for extremely low luminosity dwarf galaxies in the absolute magnitude range -13.5 > M sub(r) - 5 log h sub(70) > -16. The sample is selected from the Sloan Digital Sky Survey and consists of 101 galaxies for which we have obtained follow-up H I observations using the Arecibo Observatory and Green Bank Telescope. This represents the largest homogeneous sample of dwarf galaxies at low luminosities with well-measured H I and optical properties. The sample spans a range of environments, from dense groups to truly isolated galaxies. The average neutral gas fraction is (f sub(gas)) = 0.6, significantly exceeding that of typical gas-rich galaxies at higher luminosities. Dwarf galaxies are therefore less efficient at turning gas into stars over their lifetimes. The strong environmental dependence of the gas fraction distribution demonstrates that while internal processes can reduce the gas fractions to roughly f sub(gas) = 0.4, external processes are required to fully remove gas from a dwarf galaxy. The average rotational velocity of our sample is (v sub(rot)) = (W20 sub(i,t)/2) = 50 km s super(-1), based on H I line widths. In this luminosity range, the optical Tully-Fisher relationship has significantly more scatter compared to the baryonic relationship. By including more massive galaxies from the literature, we fit a baryonic Tully-Fisher slope of M sub(bary) 8 v super(3) sub(r) super(.) sub(o) super(7) sub(t) super(0c0.15). This slope compares well with CDM models that assume an equal baryon-to-dark matter ratio at all masses. While gas stripping or other processes may modify the baryon-to-dark matter ratio for dwarfs in the densest environments, the majority of dwarf galaxies in our sample have not preferentially lost significant baryonic mass relative to more massive galaxies.