First you must prepare your application by sacrificing a fresh goathead over an alter constructed of Limburger cheese while wearing a stuffed vulture hat. Write out the application useing any fluids resulting from step 1. Next attach your application to a messenger pigeon bound for arena net headquarters. Now while hopping on one foot make 3 rotations clockwise and two counterclockwise while singing koombya and release the pigeon.
Or you could wait till Anet gives us somewhere to sign up for the beta :P like the posters above said its only press invites for this next round. If your considered a member of the press by Anet they will probably contact you. oh and ignore the first paragraph I always wanted to give a silly responce like that.
A standard sign up style Beta is highly unlikely as that's not how ANet does things. ANet does mass testing for years while in early Alpha through late Alpha instead of inviting a few thousand people 6 months - 1 year prior to release when it's far too late to change much of anything at all. Starting in March there will be Beta Weekends, if handled how GW1 was handled, you'll simply need to preorder to get in. Obviously that's just my assumption, but everything points to that being the case. They're likely running 2 months of Beta Weekends and launching in June.
Once Beta signups are open, it will be in every single topic on MMO-Champion and GW2Guru.*
No kidding, I'd be shocked if the announcement takes 5 minutes from Anet officially announcing it to when its reposted on these forums. I'm only giving it that long because I suspect the first few to see it will need a couple minutes to sign up before they take the time to copy/paste on these forums :P