Following the Big Bang, as the Universe cooled, hydrogen and helium recombined, forming neutral gas. Currently, this gas largely resides between galaxies in a highly diffuse state known as the intergalactic medium (IGM). Observations indicate that the IGM, fueled by early galaxies and/or accreting black holes, reionized'' early in cosmic history--the entire volume of the Universe refilling with ionized gas. This thesis analyzes and develops several ways to use observations of high redshift galaxies to probe this period, the Epoch of Reionization (EoR). We examine the redshift evolution of the Ly-alpha fraction, the percentage of Lyman-break selected galaxies (LBGs) that are Lyman-alpha emitting galaxies (LAEs). Observing a sharp drop in this fraction at z ~ 7, many early studies surmised the z ~ 7 IGM must be surprisingly neutral. We model the effect of patchy reionization on Ly-alpha fraction observations, concluding that sample variance reduces the neutral fraction required. We quantify the prospects for measuring the enhanced spatial clustering of LAEs due to reionization with upcoming observations from the Hyper Suprime Cam. LBGs from that survey provide a useful comparison sample. We consider the effect of foreground interlopers'' on the clustering signal. We conclude that if HSC observes back into the EoR, the abundance and spatial clustering of galaxies and the size distribution of void regions evolve more strongly with redshift for LAEs than LBGs. Moreover, measuring the cross-power spectrum between LAEs and LBGs reduces the interloper effect. We examine line intensity mapping experiments which trace large scale structure by measuring spatial fluctuations in the combined emission, in some convenient spectral line, from individually unresolved galaxies. We develop a technique to separate ``interloper'' emissions, which these surveys are vulnerable to, at the power spectrum level, based on distortions introduced when the interloper emissions are (incorrectly) assumed to originate from the target redshift. Applying this to a hypothetical [CII] emission survey at z ~ 7, we find the distinctive interloper anisotropy can be used to separate strong foreground CO emission fluctuations.