Sony plans to offer PSN users around the world free downloads of an "unidentified content", 30 days of PlayStation Plus access to new and existing members and finally, 30 days of free Qriocity service. In the same statement, the PSN service is said to be restored "soon".
As for the hacking itself, Sony are guessing that the hackers got into the network through an "application server" and from there, they were able to get into the database servers and start grabbing data. Sony estimates that around 10 million PSN users with active credit cards tied to PSN were at risk. New security measures are being moved into place with the PSN being moved to a new physical data center, new firewalls installed and a new "Chief Security Officer".
Additionally there'll be a new PS3 firmware update and passwords will only be changeable through the same PS3 that the account was started on or via a verified e-mail address. More details at the source.