The alpha and beta stages of Age of Aincrad have not started yet. The alpha stage will consist of finding bugs and fixing initial problems in the game, probably having the first 2 or 3 floors done.
The beta stage will have more open slots for testers and will consist of a maximum of 5 floors.
Gaining access to alpha / beta
The only way to gain alpha keys are giveaways and contests held during Age of Aincrad Livestreams on Twitch as well as competitions on the official Age of Aincrad forums.