Seriously, I can't find the invite function in UI. Where is it? Do I just add people to a circle?
1. Go to https://plus.google.com/circles
2. The first rectangle before the listing of your contacts should "Add a new person"
3. Enter email address of invitee and hit Enter
4. Enter a name to associate with above email address, select Circle to add into, and hit Save
I'm not entirely sure that this is the 'correct' way - I was just looking around for a place to enter arbitrary email addresses and this seemed like it. A couple of chaps I'd added this way got in, a couple more had to try a few times, and most of them see the "we've temporarily exceeded capacity" message.
Click to pop a dialog listing the people as tags or buttons, add more if you like, then invite.
If you leave and come back, the bar isn't there.
This is the same popup shown by the Invite button on your home page when it's there, just a different way of reaching it.
But it looks like this doesn't work anymore.