Plug in the flash drive then turn on the computer and go into the BIOS (usually by pressing the Delete key at the POST screen). In the BIOS, you will need to set the flash drive as the first boot device, usually called something like "USB Hard Drive". Save and exit to reboot the system.
You will be greeted with the screen you see above which gives you two options: TXT mode or GUI mode. Select TXT mode for now.
Setup will load as normal, but there is one catch that you need to be aware of here. If you are formatting your hard drive and creating a new partition, you will need to turn off the computer immediately after the partition has been formatted (before Windows starts copying files over). Turn the system back on, boot back into TXT mode then direct Windows to leave the current file system intact. This is done because the flash drive can't copy to the new partition unless the computer is restarted and the flash drive is allowed to recognize the new partition. Strange, yes, but that's just how it works. If you aren't creating a new partition, then just carry on as usual.
Once all of the setup files are loaded, the computer will reboot. This time, select GUI mode and continue your installation as you normally would with a CD. It is important that you don't remove the flash drive until you are totally finished with the installation or you may corrupt the install and have to start over again.
This guide should allow you to quickly and easily install Windows XP on a computer without an optical drive such as a netbook. You can, however, use this method on any computer to speed up the installation process, as it is much faster to install from a flash drive versus an optical drive.
Thanks for reading and happy computing!