Enable Private Messages in your Profile

You might have seen profiles have a Send Message button near the profile picture. 

Send a Private Message

Here's how you can enable it in your profile. First, click on your Profile and click on Edit Profile.

Google+ Edit Profile

Click on Contact Settings.

Edit Contact Settings on Google+

Select the first option to display the Send Message button and the second option to enable the Send an email option (this shows next to the Report this profile option). 

Google+ Contact Settings

If you want to restrict access to this option to just people in your circles or selected individuals, click on the drop-down and select the privacy level. 

Private Contact Settings

Once you are done, click on Save and Done Editing to save these options. 

Note: Other Google+ users might still be able to mention you in posts even if you do not have this option enabled. If you want to restrict that, make the changes in the Google+ Settings page. 

Change Google+ Settings