How to do?       (http://www.murga-linux.com/puppy/viewtopic.php?t=61348)
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Insert FDD(it will be erased all the data), or USB pen drive(any size is OK, but needs 640MB free space if you install Puppy on it). 
 Next 3 step is to install Puppy on USB pen drive. Skip them for FDD. 
 (If you are running LupQ, you can use the 'Frugal Installer', skip next 3 steps) 
For the USB, format(if you can erase all the data) with any of you like. 
 If you like Windows compatibility, recommended is NTFS. 
 To do it firmly, clean up the USB device using Gparted: 
 Delete all partitions on the USB devide, 
 create new partition table (Device >> Create Partition Table) , 
 Then make new partition and format. 
Optionally, frugally install in the USB device. Make a directory, say 'puppy', at the top layer of the USB device. 
Optionally, if you like to install Puppy in the USB device, copy the required files, vmlinuz, initrd.gz, *.sfs into the new directory. 
Run from the main menu, 'System' > 'Grub4Dos'(grub4dosconfig). 
Select the FDD or the USB device for the 'Where to install' at the first dialog. 
Answer 'OK' for all the dialog. 
Reboot the PC. 
You may need to select the boot device to the FDD or the USB device