I haven't used DataGrip before, but my guess is that User is going to be your DB user, Host is going to be the IP for the Cloud SQL instance, and leave URL blank (it says in the UI there that it overrides other settings, so you shouldn't need it).

My suggestion would be to setup the Cloud SQL proxy (documentation on how to do so can be found here: https://cloud.google.com/sql/docs/mysql/connect-admin-proxy). The proxy is a binary that you'll run locally with DataGrip that will handle the communication between you and Cloud SQL.

It will walk you through setting up the proxy, which then will allow you to put 'localhost' in that Host field, while still securely connecting to your Cloud SQL instance without having to worry about other settings. If you don't do it, then you'll need to authorize the IP address of where you're connecting from in the Cloud SQL settings which is less secure.

Ok, I figured it out, and thought someone out there might find my solution useful.

Host:

The IP for your server: SQL > Overview > Connect to this instance > Public IP Address

User: root

Password: password for your database

URL: jdbc:mysql://xx.xx.xxx.xx:zzzz (x's are your IP, z's are your port number)

Read DataGrip official documentation about MySQL connections