The beta is now underway, and you can register for access at developer Psyonix's website. All you'll need to enter is your PlayStation Network ID, email address, and country (only North Americans can enter, unfortunately), though keep in mind that doing so doesn't guarantee you'll get in.
If you are accepted, you'll receive a code via email that allows you to download the beta and begin playing now. Servers are only online during the day--specifically, 9 AM to 9 PM PST--with the beta set to run until some point in early May, according to a PlayStation Blog post.
While offline play (including four-player split-screen) is included in the full version, the purpose of the beta is to test out matchmaking and servers, so you'll be limited to playing against other people online. There's also a limited amount of content--the extensive customization isn't in place, and there's only a single stadium.
Rocket League, despite having a much shorter name, plays a lot like its predecessor. Both games can be described simply as a game of soccer where you control a car that can jump and flip in the air. Based on what I've played so far, it's every bit as exhilarating as SARPBC, with the added benefit of being able to easily save replays of your best saves and goals, thanks to the PS4's Share button.
The full version of Rocket League is expected out this summer.