I am a brand new Linux user.
I downloaded the ISO file for DSL and burned it onto a disk. I successfully booted my (other) machine off this disk.
The machine that I want to make into a Linux machine has a 20 GB hard drive, currently blank.
How can I access the HD from DSL running off of the CD-drive? I think that it is formatted using the NTFS file system. The last OS on it was Windows 2000, but since then has been re-formatted.

If it does not automatically put an icon on the desktop, you might have to mount it manually. Running from the live CD, open a terminal and enter commands: (the terminal should be in one of the menus--or sometimes you can get it by simply right-clicking on the desktop)

fdisk -l ##will show you the system disks and partitions

cd /mnt ## here there might be mount points already set up--if so, then try:
mount <name_of_mountpoint>

##otherwise:
mkdir <name>
mount /dev/xxxx <name> ##where xxxx is the partition ID from fdisk--eg hda1, hda2, sda1, sda2, etc.
cd <name>
ls ##now you should be looking at the contents of that partition

I found that it is mounted, but when I use the file browser to browse it, it tells me that I don't have access to that file or directory.
What is even more interesting is that it tells me that it recognizes the 19GB Hd, and says that 17GBs are in use and 2 are free.
Does the HD need to be formatted for Linux? How would I do that?

If you want to install a Linux on this hard drive, then yes, it needs to be formated for Linux default filesystem tend to be fairly different and incompatible with Windows ones (especially NTFS). If you are a beginner, you'll maybe want to give a try with a more beginner-friendly distribution like Mandriva or Ubuntu.
Anyway, all mainstream and classical distributions have installation program which are quite explicit and straightforward.

So the best way to install a Linux is IMHO to download a Mandriva or an Ubuntu, burn it then boot on it and follow the installation instructions and all should go well and fine.