Hey, that's quite a lot of questions :-).
My HD is coming near the end of it's
life and I wondered if producing an
image of the original was all that was
required?
In general, yes. Be aware that by copying an image, you will recreate your partition(s) with their orignal size. If the new HD is bigger, you will have to make an additional partition (or expand an existing, if the filesystem supports that). If the new HD is smaller, you lose.
Also, the OS install may have to be adapted to the new partition layout (if it changed). Under Linux, this means adapting the bootloader config and /etc/fstab. Under Windows, probably something in the device manager, though you may have to reinstall in the worst case.
What's the best software to
use for this
You can use any imaging software. Under Linux/Unix, dd will work fine. Under Windows, there's loads of imaging software. See e.g. http://superuser.com/questions/99643/free-and-easy-alternatives-to-ghost
and how can I accomplish
it - can I use my other laptop for the
image file or do I need to buy an
external HD to accomplish the clone?
You should create the image file after shutting down the OS (e.g. by booting from a LiveCD or by taking out the HD). An image made from a running system will be inconsistent (there are ways around that, e.g. using Shadow copy, but that's probably overkill).
You can then transfer it to any drive with enough free space. That can be an attached external HD, or another computer, which you would probably access via some kind of network service (FTP, SMB, SSH/SFTP). Once you have the image, it's just a regular (though large) file which you can copy around as you like.
Does having several partitions of both
FAT32 and NTFS with partition magic
installed affect things at all?
Only in the sense that you should make an image of each seperately.
Is it just a matter of making the
image, swapping in the new HD and
copying the image to that?
Yes, with the above caveats.