In order to connect to PostGIS from QGIS, go to Database\DB Manager and pick DB Manager. DB Manager is a very powerful tool that lets one not only simply connect and read data from a database, but also manage the database objects, such as tables, their columns, constraints, and indexes. In this scenario, we will not go into the details of how to manage a database using QGIS DB Manger, but instead we will focus on the task and simply use it to get to the data we want exported.
First, let's make sure we can connect to our database. When you expand the database node, you will see the schemas present in the database:
If you happen to not have any connections available, you may add one by using the Add PostGIS Table(s) ...