Knoppix is it's own distro, that is it has everything you need in an OS for basic functionality. When I say "graduate" I mean wipe it, and install Debian.
Yes, you can run it from the CD - there are also mini-distros (usually used for maintenance) that fit on a floppy.
As for installing it on an hd, I recommend you hang out in alt.os.linux for a while and lurk. Read every piece of documentation you can find, Linux handles devices quite differently than winblows.
What you want to do is use Winblows fdisk to free up a partition (ie, delete/shrink partitions on your hd to create "freespace"), then use the Linux tools to create your linux partitions -> you will need, at a minimum, a lilo/grub partition, boot partition, swap, and a partition for all your other stuff. Though linux will install on very little (especially compared to XP!) I recommend having about 800mb-1gb of freespace to give yourself plenty of room to install all the necessary stuff.
Read the
Debian Install Manual for a good overview on what's required to install a linux system.