Connecting a free PostgreSQL database from Render with Azure Data Studio could be a bit tricky job. Here I'm going to show you how you can do that with no time.

Render is a hosting platform that provides free PostgreSQL for a limited time.

• First, open a Render account from here. Then sign in and go to the Render Dashboard.

• Select New from the top right corner and choose PostgreSQL here.
  

• Then you will find a window that will pop up with the following fields. Give it a Name, Other fields are optional. You can leave them blank.
  

• Scroll to the bottom and select Instance Type as Free

• Then click on the Create Database button below this section. It'll take a few seconds to create this database.
• Now open Azure Data Studio(ADS) and Install PostgreSQL extension.

• Create a new Connection on ADS, you will find a new Connection type PostgreSQL here.

• For Server Name go to your Render Dashboard and Copy this selected part between @ and / and put it you ADS server name.

• Then select Authentication type Password in ADS.
• Copy User name, Password, and Database name from Render dashboard and put it into ADS.

• That is it, click on Connect it will connect your db in Azure Data Studio(ADS) and you can see your PostgreSQL database on the ADS connection list like below.

• You can now right-click on your DB and select New Query for writing a new postgresql database query.

You can find my Video Tutorial on YouTube