Log in to your cPanel and open the phpPgAdmin tool. Then click on the PostgreSQL link at the left tree menu and log in to the Postgre server using your cPanel login details.
Next, select the database you want to import data into and click on the SQL button.
You have two options. You can either paste the SQL queries in the provided field or you can upload a local file to be executed. In order to execute a local Postgre SQL script, press the "Browse" button and locate the .sql file on your local computer.
Once you have done that, click on the "Run" button and the queries from your file will be uploaded and executed on your database.