The closed beta will be offered to "thousands of hand-selected players from Europe and the United States" and gives players the opportunity to command space as either a human or Cylon fighter. According to the game's website, in order to be considered a potential closed beta tester, players need to register at Bigpoint and fill out a detailed survey.
If you'd prefer to wait, an open beta is planned for December, Bigpoint says. Until then, closed beta users will continue to increase on a daily basis as the publisher prepares to open the floodgates later this fall.
At E3 2010, I saw Battlestar Galactica Online and was impressed. The game wasn't really there, but the technology that powers BSGO was first-class considering it's a very small, browser-based title. Hopefully, the game part will hold up, when the free-to-play MMO launches.