Update: An earlier version of this post erroneously stated that you could change your password immediately, but it's dependent on PlayStation Network being restored. You now have the ability to do so once the network is re-activated in your region. We apologise for the error.
The announcement states that your password may be changed only through the PlayStation 3 on which your PSN account has been activated. If you have never downloaded any content on that pairing of account and system, an email will be sent to the address associated with your PSN ID. That message will contain instructions on how to enable your new password and sign back in to PSN.
According to Sony's Network Entertainment VP, Eric Lempel, the update is meant to prepare users and their consoles "for when PlayStation Network is back online" -- the PSN is not operational yet. Still, we can feel some excitement brewing! We always start playing once the firmware update's done.
Update 2: See? Following the update, a phased restoration will begin. Read more here.