This guide will describe how to install a full Linux OS on an USB flash disk with permanent storage feature, i.e. the system does not lost your files after a reboot as usual live distribution does. The system is fully operable OS and transferable to any PC with all your installed and saved stuff.
There are several ways how to do it, for example using two usb keys, or making a bootable live USB key and then performing the installation (as is for example decribed here How to Install Linux OS on USB Drive and Run it On Any PC ).