The indications above have nothing to do with your problem. You are talking
about an administration task. It *must* be done as root. In other words, it
is perfectly normal that the system does not let you do that without entering
your password and you do not want to change permissions so that it becomes
possible.
Although you can indeed run a graphical file browser as root, it is not a
good advice to do so (any security bug in the graphical application run by
root let the attacker do anything to your system, like installing a rootkit).
You want to copy the file from a terminal using sudo:
$ sudo cp PATH_TO_FIRMWARE /lib/firmware
