It is possible to use a PostgreSQL database for all applications that support this database type.
The installation is not in anyway different from installation using a MySQL database. You just need to specify the database type you are using.
For example, in Drupal there is a radio button which you can use to specify which database type you want to use - mysql or pgsql. From this point on you need to use the previously created PostgreSQL database and the username added to it for the script installation.