You don't have to install Puppy (to hard disk) to use it. Simply burn the ISO to CD/DVD and boot the PC or laptop with it. Once booted, you can then install it to USB flash (see the Setup menu), so you can use it for booting the PC when a CD is not available.
You don't have to save data to hard drive to work with Puppy. You can save data to USB flash or even to Internet storage . When installed to USB flash, Puppy consumes only a little over 100 MB, or about 256 MB with OpenOffice. You can use the same USB flash (where Puppy is installed) for saving data.