Square Enix have announced via Twitter, that Final Fantasy XIV will enter its closed beta phase tomorrow for PC users. They have also confirmed that there are currently no plans for an open beta.
Those invited to the beta will be able to download the client here, so if you haven't received an invitation, you aren't likely to now, as it starts tomorrow.
Square Enix also announced that at the current time there are no plans for a PS3 beta, but they hope to do one in the future.
Source: Final Fantasy Union