$ git clone http://github.com/indirect/middleman-heroku-static-app.git mysite && cd mysite
$ bundle install && bundle exec middleman init .
$ git add . && git commit -m "brand new site"
$ heroku create && git push heroku master
$ heroku open
The only expectation is that middleman build will generate your site into ./build. That's where Rack::TryStatic will look.
You can customize the 404 page that's served if TryStatic can't find a file by editing source/404.html.erb.