If you bought your computer after July 2004, you probably have the Dell pc restore program. You access this by pressing CTRL and F11 as the machine first begins to boot, just as though you are trying to go to setup. If you have previously formatted your drive with your Win XP installation disk, you are probably out of luck if you touched the partitioning of the disk. If your computer is older than two years you do not have the Dell pc restore program.
If you have previously reinstalled Windows and do not have the pc restore program, the only way is to have the Windows XP installation disk. Use one of the methods used to contact Dell customer service and see if they will send you a new one. If that doesn't work, and you have a friend that owns a Dell with the same version of Windows XP, you can use their Win XP disk to reinstall. You will not normally need the product code in this circumstance, but if it asks for one, use the number on the side of your computer.
If none of the above helps, the only thing you can do is purchase a commercial copy of Windows XP.