Before talking about that though you should know that there's already spam out there that masquerades as Google+ invites. Sophos, the anti-virus company, reports that "spammers are sending out bogus Google+ invitations that in reality point to online pharmacies." I am so not surprised.
So, if you get an e-mail note telling you that you've got a brand, spanking new Google+ account, check the URL for that link before clicking on it. If it's not going to "https://plus.google.com/," or a similar address, don't click on it. You can get your Viagra from a local drug store a whole lot more safely.
Here's the real deal. Yes, Google is still letting people into Google+. But, it's so doing very slowly . To even have a shot at a Google+ account, the first thing you need to do is to set up a Google Profile. The only information that must be on your profile is your name and gender. This account needs to be made public.
Google, by the by, isn't going to let you have private Google Profiles for much longer anyway. Come July 31st, Google will delete all private Google Profiles.
Next, have a friend who's already on Google+. Have them add you to one of their circles via the Circle find and invite page.
Another way of doing this is to just have them create a circle just for invitations. From there, have them click to add a new person to this circle and enter your e-mail address as that person. No matter which method you use, then, have them enter an update, any update, to their Stream and select the circle you've been added to as the one to share their update with.
If all goes well you should then get an email inviting you to join. Alas, that may or may not be all you need to get in. The link in the message you get may send you a page saying, in effect, that you still can't get an account because of the demand. Don't sweat it. You're still in line for a Google+ account. Give that link another click ever six or seven hours, and eventually you should get in.
So far, my friends who've tried this have made it in within a day. I'm not saying it will always work. But, I can say that it will get you started on your way to a Google+ account. Good luck.