By now, we've already seen that pressing the green Start a hangout button does just that.
So, let's start up a Hangout and play with the controls in order to learn what they do. We'll do this in a circle where you have few or no members. And we'll open it with nothing selected to make sure it is completely private for testing purposes.
First, here are three more points from the Google Plus site about who can invite others or join hangouts: