There are a few ways to install a modern linux to a usb storage device.
One is to use tools like suggested above and how to articles from www.pendrivelinux.com
. Choices include persistence.
Another is to use the distro's own directions.
Another is to use dd to copy a hybrid iso image to the flash.
One can even use wubi to make a usb install.
What I do is just install the distro to the usb just as if it were a real hard drive. There are some gotcha's where you have to either disable the internal hard drive or be very careful when reading the installer. I use a virtual machine to be safe (and I am lazy). What you get is a complete install that will generally boot to systems that can boot to a usb hard drive. Some bios and usb devices may need to be looked at or modified by flip bit or HP's usb tool.