Cosmic variance is the intrinsic scatter in the number density of galaxies due to fluctuations in the large-scale dark matter density field. We begin by presenting a flexible analytic model of cosmic variance in the high redshift Universe ($z\sim5$--15). We find that cosmic variance in the luminosity function of galaxies at these times is dominated by the variance in the underlying dark matter halo population, and not by differences in halo accretion nor the specifics of our stellar feedback model. We also find that cosmic variance dominates over Poisson noise except for the brightest sources or at very high redshifts ($z\gtrsim 12$). We provide a linear approximation of cosmic variance via a public Python package galcv. We then develop a statistical framework that folds our model of cosmic variance into the measurement of the galaxy luminosity function. Through this framework, we forecast the performance of several major upcoming James Webb Space Telescope (JWST) galaxy surveys. We find that they can constrain field matter densities down to the theoretical limit imposed by Poisson noise and unambiguously identify over-dense (and under-dense) regions on transverse scales of tens of comoving Mpc. We then apply this framework to a real Hubble Space Telescope (HST) data set at $z=$ 6 -- 8, providing a new measurement of the luminosity function of galaxies, and for the first time, measure the underlying densities of the survey fields, including the most over/under-dense HST fields. We show that the distribution of densities is consistent with current predictions for cosmic variance. Finally, we develop the first quantitative, statistically robust framework to infer the underlying density and ionization environment of regions with elevated densities of Lyman-$\alpha$ emitters (LAEs). We apply this framework to an actual observation of 14 LAEs in a $\sim$50,000 cMpc$^3$ region at $z=$ 6.93, obtaining a measurement of that region's density and ionization state, and a constraint on the average ionization fraction of the Universe.
