Slow down, chocobo! Before applying, you need to be 18 years old, have plenty of hard drive space and an internet connection (obviously), be fluent in Japanese, English, French or German for the purpose of bug reports, and have a Square Enix ID account.
Though the current round of applications is only for the PC version, Square Enix indicates that a PS3 beta may be on the way later. And if you don't get in this time, don't worry -- the company says there will be "several rounds of tester selection, with the total number of participants increasing each time." And if there's anything Final Fantasy fans are good at, it's waiting their turn.