We investigate the properties of galaxies as they shut off star formation over the 4 billion years surrounding peak cosmic star formation. To do this we categorize $sim7000$ galaxies from $1<z<4$ into $90$ groups based on the shape of their spectral energy distributions (SEDs) and build composite SEDs with $Rsim 50$ resolution. These composite SEDs show a variety of spectral shapes and also show trends in parameters such as color, mass, star formation rate, and emission line equivalent width. Using emission line equivalent widths and strength of the 4000AA break, $D(4000)$, we categorize the composite SEDs into five classes: extreme emission line, star-forming, transitioning, post-starburst, and quiescent galaxies. The transitioning population of galaxies show modest H$alpha$ emission ($EW_{rm REST}sim40$AA) compared to more typical star-forming composite SEDs at $log_{10}(M/M_odot)sim10.5$ ($EW_{rm REST}sim80$AA). Together with their smaller sizes (3 kpc vs. 4 kpc) and higher Sersic indices (2.7 vs. 1.5), this indicates that morphological changes initiate before the cessation of star formation. The transitional group shows a strong increase of over one dex in number density from $zsim3$ to $zsim1$, similar to the growth in the quiescent population, while post-starburst galaxies become rarer at $zlesssim1.5$. We calculate average quenching timescales of 1.6 Gyr at $zsim1.5$ and 0.9 Gyr at $zsim2.5$ and conclude that a fast quenching mechanism producing post-starbursts dominated the quenching of galaxies at early times, while a slower process has become more common since $zsim2$.
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