One thing to assume is you can boot from dvd/cd or usb flashdrive. There are a couple of Linux distros dedicated to system repair even though you could use an ordinary Live CD.
aside from CloneZilla as already mentioned, they have other useful tools particularly PM.
Your external disk would best have a Linux filesystem - ext2/ext3/ext4 - to allow for large files, though NTFS read/write is reliable these days, but forget FAT32 or FAT.
Once booted from the CD it's a matter of following the prompts for the backup/restore util though of course check documentation.
Another point is if you have a way of doing a practise backup/restore, preferably another system or change over the main hard disk perhaps. It's better to know your procedure can work!
Not wanting to muddy things, you could use 'tar'. If no damage to the partition scheme then just booting from the PM CD opening a terminal, mount your main and external disks, make some suitable directories to aid seeing when and what is backed up, run a filesystem check and then tar up the chosen partitions/directories. Check out using tar if you haven't done so already.
This can be a quick way if you do something that involves just a few sub-directories so not needing the whole routine of CZ or the like which would do whole partition backups.
It happens I use a full partition backup tool for the partition information and then use 'tar' for regular backups. If any probs I just boot to the CD and delete all the directories on whatever partition, run a check and then restore the previous tar files.