You need another HDD or a fileserver (with network).
Assuming you want to backup first ata hdd on target system.
Boot Knoppix on system to be backed up- Use: knoppix 2 noswap or knoppix noswap (latter if you have enough ram + cpu and you still want to browse the web etc whilst backing up
Then mount the drive/share you want to put the backups to.
e.g. mount -t smbfs -o username=blah
dd if=/dev/hda bs=131072 | lzop -c | split -b 650m -
This creates files that are 650MB in size. You can burn these to CD-Rs. I prefer to leave a bit of unused space at the CD-R's edge (some seem to peel off there).
Note: that there are reports that dd in linux in some cases doesn't copy the last byte.
Also you may have to manually turn on DMA access on the HDD using hdparm, for speed.
To restore you do a similar thing - boot knoppix. then mount the restore drive/fileserver (readonly if paranoid).
I'm not 100% sure of the command-line parameters. But that's the general principle. I have successfully backed up and restored a number of images this way.
I use lzop because it is faster than gzip - with lzop I can get an average of 30MB/sec with an Athlon 2000XP - not far from max HDD transfer rate, for not much worse compression ratio. gzip is 2 to 3 times slower. Unfortunately lzop seems to be giving me an error in Knoppix 3.6 when I try to decompress. I'm mainly using Knoppix 3.3 though.
Don't forget: CD-Rs can be flaky backup media. Assuming a 40GB HDD compresses to 15-20GB, you'll need about 25 CD-Rs. If any of these don't work you can't restore successfully. So you may need to double the number for redundancy. That is a lot of trouble.
I actually suggest buying a few spare big HDDs and backup to them.
Per GB they're not much more expensive than CD-Rs.
100-200GB drives are about twice the price per GB compared to CD-Rs, and probably less flaky, problematic and troublesome for long term storage (plus take up less space than 150-300 CD-Rs). Just don't drop them and keep them in a safe dry + cool place (packed with dehumidifiers), e.g. data-grade fireproof safe. Buy multiple different brands of HDDs if you're paranoid.