This exemple is based on redmine container.

 1- Fire up the postgres database container :
    docker run -d --name test-postgres -e POSTGRES_PASSWORD=secret -e POSTGRES_USER=redmine postgres

 2- Fire up redmine container and pass the postgres container using --link :
    docker run -d --name my-redmine --link test-postgres:postgres redmine

 Test :

     $ docker exec -it my-redmine bash

     $ env | grep POSTGR