There should be a file with an .ISO extension. You need to use whatever program you have (like Nero) for copying to cds and you have to burn the .ISO file as an image
I'd strongly suggest that you buy an imaging program like Acronis True Image or Norton Ghost (or find a free source one) and make a full image of your hard disk before you do anything. This will let you easily get back to where you were if things go awry. Grub will overwrite your main boot record and having an easy way to copy it back and start again is a really good idea when you aren't too sure what you are doing/what's going to happen. Alternatively make sure you have all of your installation disks, service packs, updates, drivers, etc. so that you can reinstall if you have to.
and follow the installation instructions and GRUB should automatically be installed and partition the hard drive for me.
The cd will boot the program - you can run it and use it from the cd and need not install it straight away. If you decide to install it, the installation program will go through the various things and prompt you. Most of the installation programs let you resize your partitions during the installation. (I found Xubuntu's installer confusing - it talked about using "C" drive when I didn't want it going anywhere near "C" so I "chickened out" and didn't install it).
If you aren't sure what partitions you already have, I'd recommend downloading something like gparted live cd (Edit: already recommended!) and use that to have a look at the partitions you already have (or have a look in disk management in XP). If you've got a newer computer, you might have a recovery partition (and maybe a data partition as well). You need to be sure what you've got and where it is, so that you don't inadvertently install to the wrong partition.
(GRUB doesn't repartition anything - it is the bootloader and will be installed during the installation process)