In the past, Google has little success with some big projects including Google Buzz, Google Wave and even their recent +1 button. However, just like Gmail and Google Music Google tries to build interest in their services by keeping it as invite only.
Most of the services Google launch are made available in US first, just like the invites for Google Music. Similarly, Google+ is also invite only right now and you can apply for an invite directly.
There are no direct invites being sent out right now but you can get yourself an invite by visiting this link. Additionally, you can learn more about Google+ service by visiting this link.