Having two copies of your XP on separate partitions will work. If installed properly your system will give you an OS menu at bootup, and you can choose which XP to start. The menu is contained in the file Boot.ini on drive C:, which must be the partition that your BIOS is set to boot from.
BOOT.ini will be modified when you install your second XP installation. What I can't remember is how much disk space you need for your new XP installation. I think that realistically you will need 5GB of space, you might install with less, but you will likely soon run out of space. Even 5GB will fill up - look at how much space you are using on drive C: now.
Assuming you have enough space for the installation, install from the XP disk and make a new installation, (not a repair or an install over the existing install). It is a long time since I did an install, so I can't give you the steps. In any case backup your data before proceeding, just in case you end up installing over the existing XP.
Once you have both copies of XP, you can modify the Boot.ini file. First change its properties, as it is read only.
There are two parts to Boot.ini, the default load labeled [BootLoader] and the list of available OSs. The first line has the time the list will be shown before the default OS boots. You can shorten this from the default 30 seconds. Then if the default OS is not the one you want, copy the line from the OS list (the part before the = sign and paste it into the Boot Loader line.
Windows has a logical way of allocating drive letters, but you can override this by allocating drive letters using the disk management provided in XP or a third party program such as Acronis, but note that this drive letter allocation will not apply during XP installation, so look carefully at the partitions offered for installation.
Leave the default OS partition as C: Your new installation of XP will be on another drive. I have one PC with XP on drive E: and another with XP on Drive K:. This is not a problem.
If your second OS is booted and is on drive D: for example, you will see the other XP windows files on drive C:
When you boot the original XP it will be on drive C: and you will see the new XP windows files on another drive. If you leave XP to label the drives it will probably be D: (but I am not sure), anyway it doesn't matter what drive they are on because you are not going to touch them.
It is not advisable to share program installations. You will need separate installations of Firefox for example, on different drives for each OS. (Typically in the OS drive's Program Files directory)
As an aside, you can have more than two OSs on one PC. Also you don't have to have an OS on drive C: Drive C: is the partition that your BIOS boots from, and it must include certain boot files including ntldr and boot.ini (at least for XP - requirements for Vista and 7 may be different).
The initial boot process takes place on drive C: and then Boot.ini provides the information for the boot process to find and load the required OS from another partition.