When I first started work on this site with Sinatra I looked for somewhere to host it. I find thinking about the deployment process as a good way of planning and learning. For this I turned to Heroku. They offer a free tier which seemed enough for my needs and also the documentation was fantastic. Take a look at the Heroku Getting Started page to sign up, install the Heroku toolbelt and login to your Heroku account via the command line terminal.