On the SitePoint Web blog there's a new tutorial showing you how to deploy applications with Dokku on DigitalOcean in the same way that you might with Heroku.

When Heroku announced their (quite reasonable) new limits for free apps, I realized that I would have to find another source of hosting for all the small, low-traffic projects that I currently have running on Heroku. [...] Since I have such an unreasonable number of apps running on Heroku, I thought it was high time to try out Dokku. Dokku is a Heroku-like tool that allows you to deploy complex apps by simply pushing with Git.

They start with some of the differences between the Heroku setup and Dokku, mostly that Dokku uses Docker for the deployment and configuration. They then show you how to create a Dokku server on DigitalOcean: setting up the domain, making the application and deploying the app with a push and other datastore plugins.