A good activity to begin with in a Google+ Community is to use an icebreaker activity with students.
This involves encouraging students to introduce themselves and to tell the community something about themselves.

The below sample text could be used to encourage them to do this

“Welcome everyone, please make yourselves at home.

As a first step I'd like everyone to create a new post and, in it, say briefly who you are and, most importantly, please share an image with the community that says something about you, it might relate to the job you have, a hobby you enjoy, a favourite film, a photo you yourself took, a place you'd like to visit, an important time in your life, whatever. Don't overthink it (but please do it).

Once you have done it try to find something in common with at least five other students and let them and everyone else know about it by using the comment feature. Look back and try to comment on the comments others have let you.

Try to keep the conversation going.... “

   Try also to be clear with students, both inside and outside of live lectures, about what you expect them to use the Google+ Community for and consistently encourage them to make use of it.

As well as an ice-breaker activity, you could:
  1. Encourage your students to use the space to communicate about class topics, ask questions and share resources.
  2. Provide information on upcoming deadlines, useful activities, professional opportunities, etc
  3. Keep your students engaged in classroom activities by regularly posting additional resources or questions.
  4. Ask students to engage in formative assessment activities by having them post reflections on what was covered in-class, upload evidence of ongoing class work, assess and provide feedback on each others’ material, etc.