Google API authorization - how to tie it to the site?

Question

Google

Hey!
There is a website where you can fill out a special form by clicking on the link. The questionnaire was created in google drive and inserted into the page as an "iframe". The data entered in the questionnaire is stored in a google docs table.
The following is required:
- display the questionnaire only to those users who have logged in via Google
- attach a button that will allow you to take the answer to the questionnaire from the column of the same table where the data from the questionnaire is added, but it is not clear how to link the account of the person who filled out the questionnaire to the row in the table.