How can I browse my Heroku database?

Now that I've deployed my webapp to Heroku, how would I be able to browse the database as it's altered over time?

How can I see my table in Heroku Postgres?

From the application dashboard on Heroku, go to the 'resources' tab and search for postgres. Provision it and use the free option. There's now a clickable link to the Datastore associated with your application. Go ahead and open the link to your datastore, and take note of exactly how to get here again.

Where is Heroku data stored?

Heroku's physical infrastructure is hosted and managed within Amazon's secure data centers and utilize the Amazon Web Service (AWS) technology.

Try heroku pg:psql. For instructions for how to do this, see this.