http://blog.eu.playstation.com/2014/04/11/upgrade-final-fantasy-xiv-realm-reborn-ps3-ps4/
also
http://www.reddit.com/r/ffxiv/comments/22rn0k/ffxiv_ps3_to_ps4_upgrade_guide_ask_your/
A great resource!
You need a code to get the free PS3 > PS4 permanent transfer.
You get it from signing up for the transfer in the Mog Station. Then you input the code when updating the game from in the PS4 from the Playstation Store and you are good to go.
PS4 beta users do not have to redownload the client, just perform an update.
Details inside.