Quite a few moving parts to Dokku on Digital Ocean, but, thankfully, you can do most things with some simple script commands. Once your key is setup (follow the video), you can pop in the commands below. Make sure you're logged in as root.

Step 1: create the app.

dokku apps:create rails

This will set up a "host" for us, which is a bare Git repository with post and pre-receive hooks that will run when we push to it.
The next step is to add the PostgreSQL plugin:

dokku plugin:install https://github.com/dokku/dokku-postgres.git
dokku postgres:create railzdb
dokku postgres:link railzdb railz

The last line there will give you your DATABASE_URL, which you need to copy for use later.
We need to work with our remote database in order to migrate our existing data, so we might want to expose the port:

dokku postgres:expose railzdb

This will expose our Dockerized database on a random port. We can also specify one, if we want, by passing it as the second argument.

Now that we have our connection information, we can send our tables and data up to our Dokku database. The command is, thankfully, very simple, but you do need to have Postgres installed locally. If you don't, you can also use migrations and seeds, which we'll discuss later on.

psql $DATABASE_URL < ./db/db.sql