The cycling of gas into and out of galaxies is a crucial ingredient in their evolution. The incidence rate and effects of these gas flows are expected to be common and pronounced at redshifts of z ~ 2, the peak of star formation and quasar activity in the history of the Universe. In this work, I characterize cool low-ionized (~10^3 K) and warm ionized (~10^4 K) gas outflows and inflows from individual and stacks of star-forming galaxies during this epoch. I utilize rest-optical spectroscopic data from the MOSFIRE Deep Evolution Field survey and rest-UV follow-up campaigns with Keck LRIS and KCWI. Using Lyα emission, low-ionization interstellar metal absorption lines, and broad components of strong rest-optical emission lines, I measure the properties of outflows and inflows, how their properties scale with the global properties of galaxies, and the driving mechanisms behind outflows. My results indicate that mechanical energy from supernova explosions primarily drives cool gas outflows, while a combination of mechanical energy and radiation pressure acting on dusty material drives warm gas outflows. In addition, I find that warm outflows have modest mass-loss rates and are likely negligible, even during the peak of cosmic star formation history. By comparing galaxies with robust measurements of cool low-ionized gas inflows to those without inflows, I explore the low detection rate of inflowing gas. My results reveal that galaxies with inflows have higher star-formation activity and that the covering fraction of inflowing gas is enhanced among galaxies with higher specific star-formation rates. Lastly, I utilize integral field spectroscopy to measure the spectral variation of Lyα emission across stacked Lyα halos of z ~ 2 star-forming galaxies. Redshifted single-peaked Lyα profiles are ubiquitous down-the-barrel of galaxies, while farther out, the shape of the profile varies with outflow velocity and star-formation activity. Overall, my dissertation work provides a glimpse into the complex multi-phase nature of gas cycling around star-forming galaxies at z ~ 2 when feedback from star-formation activity was at its highest.