1. Open your Google+ home screen
2. Head to the “Circle” tab
3. Click “Add a new person”
4. Write down their email (preferably Google account), or maybe you can try emails from other domains
5. Pick the proper circle for your friend
6. Head back to the home screen, then write your friend’s email on the stream

There’s another alternative if you want to sent all-at-once invitation, just repeat the step 1-5. Then you can sent the invitation to the circle instead of writing down the emails one by one.