Square Enix has revealed the details on how players can upgrade their PS3 copies of Final Fantasy XIV: A Realm Reborn to the PS4 version for free, and you can do so from now up until the end of the year at least. Before you go through the upgrade process you must have logged into the PS3 version at least once so details are up to date. After the upgrade you will no longer be able to play the PS3 version of FFXIV: A Realm Reborn.
To begin the process log in to your Square Enix account at Mog Station, click on the banner advertising the PS3 to PS4 upgrade, read through the text presented to you about what will happen to your account once upgraded. Then you’ll be presented with the upgrade option, and you have to make sure you are using the account you want to upgrade because it can only be done once. After it’s all confirmed you’ll be given a promotional code to download the game from the PS Store for PS4. Your subscription will carry over.
Some people have been commenting on the blog post that you can pick up the PS3 version of FFXIV pretty cheap from various retailers, and then use the upgrade option, so that’s one way to do it.
Source: PS Blog