This is the simplest possible init file that demonstrates switch_root usage:
# First, find and mount the new filesystem.
mkdir /newroot
mount /dev/whatever /newroot
# Unmount everything else you've attached to rootfs. (Moving the filesystems
# into newroot is something useful to do with them.)
mount --move /sys /newroot/sys
mount --move /proc /newroot/proc
mount --move /dev /newroot/dev
# Now switch to the new filesystem, and run /sbin/init out of it. Don't
# forget the "exec" here, because you want the new init program to inherit
# PID 1.
exec switch_root /newroot /sbin/init