You should already be logged into root. Just type su (then enter). If it is asking you for a password at boot, there is something wrong when you made the live USB.
when I try to run 'airmon-ng start wlan0' in the terminal, it's asking me 'run it as root'. Then I 'su' or 'su root', but then it's asking me for password. - Xiaopan 0.4.3b - usb was created by lili