Welcome to the forums! What is your level of Linux knowledge? Do you know about mount
command? (man mount) DSL does not have automatic device mounting like Ubuntu (or automatic much of anything, that is why it is tiny), so you must manually create a mount point and use the mount command.
Ubuntu runs fine from USB and is maybe an easier beginner project; read here: http://www.ubuntu.com/download/help/...tick-on-ubuntu
If you do not set up persistence then all files/settings will be lost on shutdown (you must store them to the "cloud" or to a separate filesystem that is encrypted) and your USB will be totally safe/private.