Square Enix has a two-phase beta lined up for Final Fantasy 14: A Realm Reborn on PS4, with the first beginning alongside the console's launch in Japan on February 22. The good news is the beta is open to all PS4 owners, and the first phase lasts over a week.
That opening phase is scheduled for February 22 to March 3, the second April 4-7 - those phases are tied to Japanese Standard Time, so the US and Euro dates may be a day earlier. While the first phase ends with a character wipe, players can transfer their Eorzean heroes from the second phase into the retail game, which launches the week following on April 11.
As for upgrading your PS3 copy of A Realm Reborn, you can do it as soon as the PS4 version launches and it won't cost you a dime, but you lose access to the PS3 version as a result.