ABSTRACT The results of a multifaceted search for spectral-line emission from galaxies at high redshift are presented. Deep two-dimensional spectra of four blank sky fields were taken at the Muliple Mirror Telescope (MMT) at wavelengths corresponding to redshifted Lyman alpha emission in the range 2.7 < z < 4.7, and the resulting nondetections are used to place upper limits on the space density of randomly distributed Ly-alpha emitters. Although the predictions of a conservative model of galaxy formation incorporating cold dark matter are not excluded in a statistical sense, the search would have detected star-forming dwarf galaxies comparable to the Magellanic Clouds at z = 3, given minimal extinction by dust. The Goddard Fabry-Perot Imager, a piezoelectrically controlled tuneable narrow-band filter system with a stand-alone CCD, was developed and tested, and used a the Kitt Peak National Observatory (KPNO) 4-m telescope to image the damped Ly-alpha absorbing clouds toward three high-redshift QSOs in the light of redshifted Ly-alpha. A companion galaxy to one of the damped systems was discovered, confirmed with follow-up spectroscopy, and its properties are presented and discussed. The companion exhibits strong Ly-alpha and weak C IV lambda-1550 and He II lambda-1640 emission lines, and is apparently producing stars at a rate of 5-10 solar mass yr-1. The implications of the companion's proximity to the damped cloud are analyzed in view of the previous nondetections, and a lower limit to the spatial correlation function of the damped Ly-alpha systems with galaxies is given. Spectroscopic limits on Ly-alpha emission from seven damped systems, including some known to have low chemical and dust abundances, imply levels of star formation lt 1 solar mass yr-1, but extinction by dust in some cases may cause an underestimation of these rates. With near-infrared spectrographs at the MMT and the KPNO 4-m telescope, eight damped Ly-alpha systems were searched for spectral lines characteristic of star-formation regions but redshifted from the optical into the near infrared. A possible detection of [O III] lambda-3727 and H-beta from one system implies a star-formation rate on the order of 100 solar mass yr-1, though the remainder of the observations produced nondetections. The implications for galaxy formation and evolution at high redshift are discussed.