$ sudo mount /dev/sdb* /mnt
$ ls /mnt
backup-rsync
$ sudo rsync -aHAXS --delete-before /* /mnt/backup-rsync --exclude={/dev,/mnt,/media,/proc,/run,/sys,/srv,/tmp,/var/run,/home/$user/my-homedir-mntdir}
This is how I backup my laptop, using rsync. Ideally you want 2 (at least) backup locations and backup to each on alternate occasions. Possible problems: if you don't exclude the backup location dir it recursively copies itself and fills it up. Once I modified the exclude bit but forgot to add the closing } bracket back on which meant that part was completely ignored. So it filled up the backup drive partition. When I got this error message I killed the process and went to delete everything in the partition but because of some weird effect probably due to dev and so on being copied, it went completely mad and started deleting my OS on /, I noticed when the desktop started disappearing and hit ctrl c. Somehow I managed to recover most things from the remains... so be careful not to get a typo like that.
I think I will try btrfs snapshots soon, a lot of people seem to like those for backups but not tried them myself yet.