# in the current system, make a location for the installer data
sudo mkdir /inst
sudo chown -R $USER: /inst

# download installer kernel
cd /inst
wget http://ftp.debian.org/debian/dists/stable/main/installer-amd64/current/images/SHA256SUMS
mkdir hd-media; cd hd-media
wget http://ftp.debian.org/debian/dists/stable/main/installer-amd64/current/images/hd-media/vmlinuz
wget http://ftp.debian.org/debian/dists/stable/main/installer-amd64/current/images/hd-media/initrd.gz
cd ..

grep hd-media/vmlinuz SHA256SUMS | sha256sum -c - || echo DO NOT INSTALL THIS
grep hd-media/initrd.gz SHA256SUMS | sha256sum -c - || echo DO NOT INSTALL THIS

# find out the hard drive where you put the installer kernel
df /inst
# /dev/sda  --> hd0
# /dev/sda5 --> hd0,msdos5
# note that sda does not necessarily correspond to hd0, only probably does.
root_str="hd0,msdos5"

# add a grub entry so grub boots the installer kernel.
# This is telling grub to look at your current system's partition, fetch the
# kernel from there and then launch that.
# In short, make sure to append to the existing 40_custom file.
# In long: the /etc/grub.d/ files are IMHO made unnecessarily complex.
# They are shell scripts expected to *output* grub menuentries to *stdout*. The
# 40_custom file has a line saying
#   exec tail -n +3 $0
# which runs tail to output this same file starting from the third line.
# It really is a madly convoluted way to let you write menuentries in
# plain text: grub launches 40_custom as shell script, which then finds
# out its own filename with `$0', feeds it to tail to start reading from
# line 3, and thus prints the rest of the file to stdout.
# We might have just written the menuentry to /boot/grub/grub.cfg, but anyone
# running update-grub would overwrite that. So append the menuentry after that
# `exec tail...` in /etc/grub.d/40_custom:

sudo sh -c 'cat >> /etc/grub.d/40_custom' <<END
menuentry 'Installer' {
  insmod part_msdos
  insmod ext2
  set root='($root_str)'
  linux /inst/hd-media/vmlinuz
  initrd /inst/hd-media/initrd.gz
  echo "Installer"
}
END

# flush /etc/grub.d into /boot/grub/grub.cfg.
sudo update-grub

# At this point, you could already reboot your machine and select the
# 'Installer' item in the grub boot menu -- but to work, it still needs an ISO.
# (a file system image with debian packages). It will actually start looking
# for it in the root directories of all hard drive partitions it can find.
# Other distros may need a more specific setup to find the installation
# packages, but for debian, it is sufficient to just drop the installer .iso
# file in any root partition. e.g.:
wget https://cdimage.debian.org/debian-cd/current/amd64/iso-cd/debian-8.7.1-amd64-netinst.iso
wget https://cdimage.debian.org/debian-cd/current/amd64/iso-cd/SHA256SUMS
grep debian-8.7.1-amd64-netinst.iso SHA256SUMS | sha256sum -c - || echo DO NOT INSTALL THIS
sudo mv debian-8.7.1-amd64-netinst.iso /

# That should be it. Reboot and select the "Installer" menu entry when grub
# comes up.