Navigate to the Google Cloud SQL console to find your list of instances.
The public IP address, if available, will be your database hostname.
If your instance does not have a public IP address, you will need to check further how to connect to it by clicking on the hamburger menu and selecting Edit.
By expanding the Connections dropdown in the Overview section you can see the network setup of your database. In the example below, this instance has a public IP and any IP address can connect to it. In most setups, you would restrict what IPs can connect to your database.
Select the Users tab in the left menu to see what users are available in the Postgres database. The
postgres user is the root user.
When you first created the Postgres instance on Google Cloud, you would have received credentials for the root user or input them yourself. If you do not have them, you can change the credentials by selecting the three dots next to the user you want to change.
By now you have obtained the hostname, user, and password for your database and you can use a client like Arctype to connect!