Both operating systems cannot coexist on the same partition
That's not true,
This tool will install Ubuntu on one of your Windows partitions. The program will do some stuff with your Windows bootloader so that you'll be able to use Ubuntu (native, not emulated!) without having to partition your hard drive. Ubuntu will be stored in one big file if you choose this option. The downside? You won't be able to access your
Ubuntu files from Windows XP. (Yes, it is possible to use your Linux partitions on Windows as if they were regular Windows partitions.)
Once I get the hard drive installed (note it is going to be a slave) how should I format it? The total drive size is about 80 GB. Should I leave it as one partition or do two?
The installer actually has a built-in partitioning program and I believe that the setup wizard will automatically offer you to do the partitioning work automagically. If you decide to it manually, first create a big ext3 partition (let's say 99% of your free space). If the setup should ever ask for its so-called "mount point", enter a forward slash ("/"). You'll soon see that this is something like drive letters in Windows. Usually, your primary partition would be called "C:\". In Linux, we just call it "/". Anyway, secondly you'll also need a swap partition. This is some kind of secondary memory (in Windows, this is called a swap file I believe).
Finally, once I have installed Ubuntu, how do I setup up a dual-boot?
There's no need for that, Ubuntu will automatically detect Windows XP. After you've installed Ubuntu, you can choose between Ubuntu and Windows on startup. Ubuntu's the default option, but there's a tweak for this.
Do I download from the official site and install from there or do it on a CD?
Download the ISO on their site
(make sure that you pick the correct version and architecture, see ubuntu.com for details), burn it using a CD burning program that can handle these files (such as
CDBurnerXP Pro), reboot your computer and boot off the CD.
Does Ubuntu have its own audio player?
Sure, there are tons of them actually!

By default, Totem is installed on your computer but you can always install more players if you want.
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Quick summary: just download the correct ISO and start the installer. Don't worry about partitioning or dual booting, the setup will take care of that.