  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 $z\geq1.2$. 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.
