Sony began taking applications for the Playstation Home closed beta program today. The company is currently only accepting Japanese PS3 owners for the beta program.

Applicants must be over 18 and apply by August 11th to be considered for a random selection to gain access to the new Sony 3D online world. Sony still plans to go open beta with Playstation Home this fall.
The beta of Playstation home will feature Namco Museum BETA with classic games of Pac-Man, Galaga, moth, DigDug and Elevator Action.
Via this Sony announcement (Japanese).

I assume Sony will also conduct a closed beta program outside of Japan in North America and Europe at some point. More details about the Sony Playstation Home is available on the Japanese Playstation Home site.