People can sign-up to receive “exclusive” information regarding the service that will most likely result in beta information. First, you’ll need to go to the website and from there you’ll be asked to enter such information as your first and last name, zip code, email address, and PSN ID. You’ll then be automatically registered and be kept “up with the latest news and updates on the evolution of PlayStation Now in the future” and “to be the first to receive exclusive information on PlayStation Now.”
This certainly does not guarantee beta entry but it doesn’t hurt to sign up anyway.