You will need a Google+ account for that and most people report that the loophole, which allowed many to sneak in despite not having invites, has been closed.
Still, you can head over to the XDA-Developers forum topic and get the Google+ app, version 1.0.2. The app is better than the mobile site because it receives instant notifications, Huddles are enabled, too (that’s the group chat feature).
Also, whatever photos you snap with your droid are automatically uploaded and once that’s done, you can share them on Google+ from any device. There’s an option to switch that off if you want.
Anyway, grab the app and give it a spin. Don’t forget to share your thoughts on it in our comments.
Update: Well, it seems Google unleashed the Google+ app to a much wider market than I initially thought. So, check the Android Market first, it may be available. And if it’s not, then you can grab it from XDA-Developers.