By using a Linux distro, like Knoppix, that boots up from a CD - how does one store files when Knoppix is running? i.e. the hd has not been partitioned.
You have to partition it. Various partitioning tools maybe bundled with any given distro. Partition your disk, format the proper partitions (again, formatters are bundled), and proceed to mount them (the fat kernels that auto include all the modules will recognize most formats).
USB storage works great for that. Just plug it, save it, take your Knoppix to the next machine. Restore from there your configuration and files.
What if I to use an app not included with the Knoppix distro - i.e. say Eclipse.
Generally those LiveCD distros are to let you try the software out. If you like it, just install it and then you can install all the software you want. With Knoppix, it's really easy to get new software once you do a hd-install.
I think that if you are wanting to use an app not on a distro like Knoppix, but aren't willing to commit to installing Linux on your system yet that you either see if they have a Windows version (like Eclipse and Thunderbird and Firefox) or see if it can be run using Cygwin. A good majority of apps can be run through Cygwin which can run on your Windows box without messing up your system.
coLinux <http://colinux.org> will let you but a full-fledged Linux inside your Windows box (and recently, inside your Linux box as well). It's not polished, and not yet perfect, but if you want to experiment, give it a try.
With Knoppix, you can save your configuration on a USB device, or on a Windows disk within an image file (well, on my disk, the image got unreadable, I wonder why). I'm not sure it would be a good idea to store something like Eclipse, but I suppose it could be done.
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