Thoughtbot posted this a few weeks ago:
You need the pgbackups addon (free), and use this to transfer from production to staging
heroku addons:add pgbackups --remote staging
heroku addons:add pgbackups --remote production
heroku pgbackups:capture --remote production
heroku pgbackups:restore DATABASE `heroku pgbackups:url --remote production` --remote staging
Gist here: https://gist.github.com/1095522
Edit: Make sure you have your git branches "staging" and "production" pointing to the heroku apps.
git remote add production production_heroku_app
git remote add staging staging_heroku_app