  Few galaxies have been found between the redshift ranges z < ~1 probed by
magnitude-limited surveys and z > ~3 probed by Lyman-break surveys. Comparison
of galaxy samples at lower and higher redshift suggests that large numbers of
stars were born and the Hubble sequence began to take shape at the intermediate
redshifts 1<z<3, but observational challenges have prevented us from observing
the process in much detail. We present simple and efficient strategies that can
be used to find large numbers of galaxies throughout this important but
unexplored redshift range. All the strategies are based on selecting galaxies
for spectroscopy on the basis of their colors in ground-based images taken
through a small number of optical filters: GRi for redshifts 0.85<z<1.15, GRz
for 1<z<1.5, and UGR for 1.4<z<2.1 and 1.9<z<2.7. The performance of our
strategies is quantified empirically through spectroscopy of more than 2000
galaxies at 1<z<3.5. We estimate that more than half of the UV-luminosity
density at 1<z<3 is produced by galaxies that satisfy our color-selection
criteria. Our methodology is described in detail, allowing readers to devise
analogous selection criteria for other optical filter sets.
