While implementing the G+ sign in on my site, there were a few "need to know" things that were buried in the documentation.
Hopefully this helps someone.
I'm using the HTTP API.
The "old" system uses the scopes:
https://www.googleapis.com/auth/userinfo.profile https://www.googleapis.com/auth/userinfo.email
whereas the new one uses:
https://www.googleapis.com/auth/plus.login https://www.googleapis.com/auth/plus.me<
Update: Actually you still need to use
https://www.googleapis.com/auth/userinfo.email
auth/plus.me does return a bunch of useful profile information, though.
You'll see the auth/plus.login fairly quickly while reading the API docs, but mention of the auth/plus.me is a little buried.
In the docs the person GET request looks like
GET https://www.googleapis.com/plus/v1/people/userId
 
If you're just using auth/plus.login scope, you'll have to request the userid and then make a separate API call to get the person's info. (
OR you use auth/plus.me scope and set "me" as the userid in the GET request.
 
I'll update this as I experiment with the API some more.
 
If you'd like to add anything, leave a comment.
 
related links:
https://developers.google.com/+/api/latest/people/get#examples
https://googleplusplatform.blogspot.com/2013/02/google-plus-sign-in.html