Shock breakout is the brightest radiative phenomenon in a supernova (SN) but is difficult to be observed owing to the short duration and X-ray/ultraviolet (UV)-peaked spectra. After the first observation from the rising phase reported in 2008, its observability at high redshift is attracting enormous attention. We perform multigroup radiation hydrodynamics calculations of explosions for evolutionary presupernova models with various main-sequence masses $M_{rm MS}$, metallicities $Z$, and explosion energies $E$. We present multicolor light curves of shock breakout in Type II plateau SNe, being the most frequent core-collapse SNe, and predict apparent multicolor light curves of shock breakout at various redshifts $z$. We derive the observable SN rate and reachable redshift as functions of filter $x$ and limiting magnitude $m_{x,{rm lim}}$ by taking into account an initial mass function, cosmic star formation history, intergalactic absorption, and host galaxy extinction. We propose a realistic survey strategy optimized for shock breakout. For example, the $g$-band observable SN rate for $m_{g,{rm lim}}=27.5$ mag is 3.3 SNe degree$^{-2}$ day$^{-1}$ and a half of them locates at $zgeq1.2$. It is clear that the shock breakout is a beneficial clue to probe high-$z$ core-collapse SNe. We also establish ways to identify shock breakout and constrain SN properties from the observations of shock breakout, brightness, time scale, and color. We emphasize that the multicolor observations in blue optical bands with $sim$ hour intervals, preferably over $geq2$ continuous nights, are essential to efficiently detect, identify, and interpret shock breakout.
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