To use PostgreSQL as your database in Python applications you will need to use the psycopg2 package.
$ pip install psycopg2
$ pip freeze > requirements.txt
And use this package to connect to DATABASE_URL in your code:
import os
import psycopg2
import urlparse

urlparse.uses_netloc.append("postgres")
url = urlparse.urlparse(os.environ["DATABASE_URL"])

conn = psycopg2.connect(
    database=url.path[1:],
    user=url.username,
    password=url.password,
    host=url.hostname,
    port=url.port
)