  We develop a general strategy for constructing the explicit Local Langlands
Correspondences for $p$-adic reductive groups via reduction to LLC for
supercuspidal representations of proper Levi subgroups, using Hecke algebra
techniques.
  As an example of our general strategy, we construct the explicit Local
Langlands Correspondence for the exceptional group $G_2$ over a nonarchimedean
local field, with explicit $L$-packets and explicit matching between the group
and Galois sides. We also give a list of characterizing properties for our LLC.
In \cite{G2-stability}, we complete unique characterization using stability
property of our $L$-packets. For intermediate series, we build on our previous
results on Hecke algebras. For principal series, we improve previous works of
Muic etc. and obtain more explicit descriptions on both group and Galois sides.
  Moreover, we show the existence of non-unipotent \textit{singular}
supercuspidal representations of $G_2$, and exhibit them in \textit{mixed}
$L$-packets mixing supercuspidal representations with non-supercuspidal ones.
Furthermore, our LLC satisfies a list of expected properties, including the
compatibility with cuspidal support.
