There is no clear-cut criterion for getting into the private beta, but users registering should have a 5 Mbit internet connection and a PlayStation 3 console.
Sony has begun inviting users to beta test the PlayStation Now streaming service. Interested users can still register to get access to the exclusive beta from here. However, it looks like Sony is sending out invites based on regions, with most users in the Los Angeles and Washington D.C metro areas getting successful invites as of now.
From invite e-mails posted on Neogaf, it looks like the minimum requirement to be a beta tester involves having a 5 Mbit wired broadband connection and a PlayStation 3 console. The Gaikai-based streaming service is said to stream games older PS titles to current-gen consoles, but that functionality is said to be added at a later stage. Currently, PlayStation Now will only stream PS 3 games.
The PlayStation Now service does have the potential to be a huge success, but for it to take off, Sony has to ensure that it is not priced too high, while having a strong catalogue of games available for streaming.