[clang-tidy] Separate the check-facing interface

Summary:
Move ClangTidyCheck to a separate header/.cpp
Switch checks to #include "ClangTidyCheck.h"
Mention ClangTidyCheck.h in the docs

Reviewers: hokein, gribozavr, aaron.ballman

Reviewed By: hokein

Subscribers: mgorny, javed.absar, xazax.hun, arphaman, jdoerfert, llvm-commits, cfe-commits

Tags: #clang, #llvm

Differential Revision: https://reviews.llvm.org/D59714

llvm-svn: 356890