Steps to get a sinatra/datamapper site running on heroku.  First do git init in a directory then you need 3 files: A Gemfile with the gems used, make sure to group them since sqlite isn't available on heroku.

source :rubygems
gem 'sinatra'
gem 'thin'
gem 'haml'
gem 'datamapper'
gem 'dm-postgres-adapter', :group => :production
gem 'dm-sqlite-adapter', :group => :development

A Procfile, simply tells heroku which file to start with, note the -e production to put the site in production mode (in case you load different dependencies depending on environment)

web: bundle exec ruby demo.rb -p $PORT -e production

And a simple Sinatra site

require 'sinatra'
require 'haml'
require 'datamapper'

class Item
  include DataMapper::Resource

  property :text, String,:key => true
end

configure do
  DataMapper.setup(:default, ENV['DATABASE_URL'] ||
                             "sqlite3://#{Dir.pwd}/demo.db")
  DataMapper.finalize
  DataMapper.auto_migrate!

  Item.create(:text => "hi")
end

get '/' do
  @demo = Item.all

  haml :view
end

Install heroku toolbelt, then do the following:

heroku login
heroku create
heroku addons:add heroku-postgresql:dev
heroku pg:promote HEROKU_POSTGRESQL_BROWN

The last command sets the DATABASE_URL environment variable to point to the added postgres instance, the name depends on the added instance type use heroku config to get the correct one. Once all these things are done you can push the site to heroku.

git push heroku origin

For local testing start the site with this command

bundle exec ruby demo.rb

I've put a demo repo for the sinatra site in a github repo here