@DTing's answer is correct that Google's docs encourage you to use a local MySQL from the local development server and recommend that pattern.
However, if you disagree and want to run the development server against your "production" SQL in the cloud, that's supported, too (just not encouraged because a bug during development could destroy your production data!).
Specifically, you follow the general instructions at, and pointed to by, https://cloud.google.com/sql/docs/getting-started#work (ignoring the appengine-specific part): make sure your Cloud SQL instance has an IP address, enable the outside-visible IP address of your workstation, make sure the SQL instance has a root password -- then check everything is working with a command line MySQL client, e.g
[[Note: to verify your workstation's outside-visible IP address, use e.g a browser to visit a site such as http://checkmyip.com/ ]]
$ mysql --host=INSTANCE_IP --user=root --password
and once everything is set up properly you just follow the instructions at https://cloud.google.com/appengine/docs/php/cloud-sql/#PHP_Using_a_local_MySQL_instance_during_development :
To connect to a Cloud SQL instance from your development environment,
substitute "127.0.0.1" with the instance IP address. You do not use
the "/cloudsql/"-based connection string to connect to a Cloud SQL
instance if your App Engine app is running locally in the Development
Server.
If you want to use the same code locally and deployed, you can use a
Special $_SERVER keys variable (SERVER_SOFTWARE) to determine where
your code is running. This approach is shown below.
So for example if your Cloud SQL's IP address is 12.34.56.78, you'd use
$sql = new mysqli('12.34.56.78:3306',
'<username>',
'<password>',
<database-name>
);
when $_SERVER['SERVER_SOFTWARE']
is not set or does not contain Google App Engine
(which means you're running on the local development server).