Working on the basis that you've got your backup drive mounted on /backup you'll probably
want something like:
rsync -ar --exclude "/backup/*" --exclude "/proc/* --exclude "/sys/*" / /backup/
This will generate the backup.
Grub only needs setting up once on the drive as it reads from /boot/grub to get the settings,
unlike lilo which writes the config to the boot sector.
Running grub and getting the grub console you should be able to do:
grub> root (hd1,0)
grub> setup (hd1)
This will set your 2nd drive to boot from its 1st partition.
You can then run the rsync whenever you want, if you update grub I'd recommend running the
grub procedure again.