The Dense Basis SED fitting method reveals previously inaccessible information about the number and duration of star formation episodes and the timing of stellar mass assembly as well as uncertainties in these quantities, in addition to accurately recovering traditional SED parameters including M*, SFR and dust attenuation. This is done using basis Star Formation Histories (SFHs) chosen by comparing the goodness-of-fit of mock galaxy SEDs to the goodness-of-reconstruction of their SFHs, trained and validated using three independent datasets of mock galaxies at z=1 from SAMs, Hydrodynamic simulations and stochastic realizations. Of the six parametrizations of SFHs considered, we reject the traditional parametrizations of constant and exponential SFHs and suggest four novel improvements, quantifying the bias and scatter of each parametrization. We then apply the method to a sample of 1100 CANDELS GOODS-S galaxies at 1<z<1.5, finding that 15% of the galaxies in our sample exhibit multiple episodes of star formation, with this fraction decreasing above M*>10^9 M_sun, in contrast to current simulations. About 40% of the CANDEL galaxies have SFHs whose maximum occurs at or near the epoch of observation. These results are presented in Iyer and Gawiser (2017, ApJ 838 127), available at https://arxiv.org/abs/1702.04371