Note: This procedure has worked for me on 30 June, 2011 and 1 July, 2011. Things are very much in flux at Google with this beta release product, so these instructions may not work later, or there may later be better ways to actually invite people.
Google likes to release new stuff as beta testing and start by inviting just a few people. I think Gmail was in beta for four years or something. Right now, Google Plus is in beta, and it doesn’t really make sense that Google is being stingy with the invites. After all, what’s the point of a social networking site if “no one” is using it? So here is how I’ve invited people.
Click on Share in the top-right corner and write something (anything). Below that, paste in the email address of the person you’re trying to invite. Confirm it, and it’ll turn blue. Then click the green Share button.
That’s it. Please don’t post in the comments begging me to invite you. Beg your friends to read this tutorial instead.