The alpha server is currently whitelist access only. We don't have a set process for getting whitelisted (yet).
But generally,
If you are an active, social player who loves to play games for fun and relaxation rather than to win...
If you have been ranked past 'Cool' on the classic server...
If you are actively involved with Team9000... ( hanging out on the forums, during the casts )
If you are over 18...
If you are on the Mumble...
If you are not a douche...
Then you are probably already on the whitelist.