create a new repository on https://github.com

$ cd ~/projects/rails

$ rails new project_name

$ cd project_name

$ git init

$ touch README.md

then fix file of Gemfile README.md and .gitignore  to lets it adapt to your project environment

$ git add . 

$ git commit -m "Initial commit"

$ git remote add prigin https://github.com/<username>/project_name.git

$ git push -u origin master

deploy on heroku:

$ heroku create project-name

$ git push heroku master

$ heroku urn rake db:migrate