if you want to boot from a portable hdd that is possible. IF (!!) your computer supports that! I don't know if you are familiar with terms like motherboard and BIOS, but if you are, here you go:
first off you must hope that your motherboard can:
1) read and use a USB drive during the BIOS startup (you know, at the beginning :P )
2) boot from it
now, my motherboard (ASUS p4p800vm) can do both and he is quite old already (2 years) so if your comp is younger than that chances are that you can boot from external USB hdd. I do not have firewire, so I do not know how that is handled...
ok, on to the next step. I know that Mandriva has some kind of distribution available that you can just download and copy on your portable hdd and it will boot from it automatically and all that stuff, but since I have no portable HDD I never tested it. I only remember seeing it on their (old) site somewhere a long time ago, so if you want more information you should ask about it in the mandriva forum here on linuxquestions.org.
note: be sure to tell your BIOS to try and boot from the external harddrive before trying the internal harddrive or you will never get the chance to boot from your external hdd. I have to plug in my drive (it is a 256 MB memory stick, a complete live distro doesnt fit on it :P , at least not a large one) before I start up the computer or the BIOS will not know it exists and will not display it as a boot option. remember to restore your settings after you plug out the external hdd because your settings can be a little messed up.
ok, good luck with you linux live distro!
ps; if it doesnt work you can always try to boot knoppix: get your copy from http://www.knoppix.net/get.php
(burn the image to cd if you downloaded it) and boot up from the cd! at the prompt where you are asked to press enter remember to type:
knoppix wheemlouse if you have a wheelmouse
knoppix toram if you have 1GB or more of ram
knoppix toram wheelmouse if you have both
if the toram option gives you problems, reset the computer and leave it out. (I had that once on a pc of a friend).
knoppix should give you a reasonable idea of what linux is like.