We isolate a set of quasars that exhibit emergent C IV broad absorption lines (BALs) in their spectra by comparing spectra in the Sloan Digital Sky Survey (SDSS) Data Release 7 and the SDSS/BOSS Data Releases 9 and 10. After visually defining a set of emergent BALs, follow-up observations were obtained with the Gemini Observatory for 105 quasars. We find an emergence rate consistent with the previously reported disappearance rate of BAL quasars given the relative numbers of non-BAL and BAL quasars in the SDSS. We find that candidate newly emerged BALs are preferentially drawn from among BALs with smaller balnicity indices, shallower depths, larger velocities, and smaller widths. Within two rest-frame years (average) after a BAL has emerged, we find it equally likely to continue increasing in equivalent width in an observation 6 months later (average) as it is to start decreasing. From the time separations between our observations, we conclude that the coherence timescale of BALs is less than 100 rest-frame days. We observe coordinated variability among pairs of troughs in the same quasar, likely due to clouds at different velocities responding to the same changes in ionizing flux, and the coordination is stronger if the velocity separation between the two troughs is smaller. We speculate that the latter effect may be due to clouds having on average lower densities at higher velocities owing to mass conservation in an accelerating flow, causing the absorbing gas in those clouds to respond on different timescales to the same ionizing flux variations.