Linking Google Account to data in my databse

I am learning mobile application design and i am having some difficulty figuring out how some problems are solved. I appreciate these questions are quite basic but I have to start somewhere!

I have developed basic web applications before but there are some differences between this and a mobile app.

Mobile app is pretty standard: 1. users logs into the application using google (O-auth). 2. User then reads and saves data to the cloud, via an api that communicates with a mongo database.

My question is:

Once a user is logged in, how do i ensure that: 1. no non registered users can communicate with the api? 2. what is the best way of associating data in the database with a particuar user? email Address, some form of identifier or something else?