To get started, you need a Google+ account. You can visit this link to get to easily get to a hangout or click on More and select Hangouts from any page in Google+.
Another very useful and cool feature is the ability to do a Hangout On Air. This will allow your hangout to be broadcast on your Google+ stream and on your YouTube channel. This is great for sharing with a large audience. It will also allow you to save the hangout to your YouTube channel where you can share the link or make it available for others to see in case they missed it. Hangouts On Air are great ways to host webinars and share PD or host study sessions for students. If you do use Google+ with students, please be aware that there is a strict over 13 policy in place. Students under 13 should not use Google+.
At the very minimum, you should definitely check out the hangouts that are happening live on Google Education On Air. Learn from educators across the globe for free. In case you missed it, you can always watch the recorded shows.
Hopefully I'll be "Hanging" out with you very soon!