We used the time since infall (TSI) of galaxies, obtained from the Yonsei Zoom-in Cluster Simulation, and the star formation rate (SFR) from the Sloan Digital Sky Survey Data Release 10 to study how quickly the star formation of disk galaxies is quenched in cluster environments. We first confirm that both simulated and observed galaxies are consistently distributed in phase space. We then hypothesize that the TSI and SFR are causally connected; thus, both the TSI and SFR of galaxies at each position of phase space can be associated through abundance matching. Using a flexible model, we derive the star formation history (SFH) of cluster galaxies that best reproduces the relationship between the TSI and SFR at z ~ 0.08. According to this SFH, we find that galaxies with M* > 109.5 M⊙ generally follow the so-called "delayed-then-rapid" quenching pattern. Our main results are as follows: (i) part of the quenching takes place outside clusters through mass quenching and preprocessing. The e-folding timescale of this "ex situ quenching phase" is roughly 3 Gyr with a strong inverse mass dependence. (ii) The pace of quenching is maintained roughly for 2 Gyr ("delay time") during the first crossing time into the cluster. During the delay time, quenching remains gentle, probably because gas loss happens primarily on hot and neutral gases. (iii) Quenching becomes more dramatic (e-folding timescale of roughly 1 Gyr) after delay time, probably because ram pressure stripping is strongest near the cluster center. Counterintuitively, more massive galaxies show shorter quenching timescales mainly because they enter their clusters with lower gas fractions due to ex situ quenching.