Based on this tutorial.

Step One

Update aptitutde:

sudo apt-get update

Install curl:

sudo apt-get install curl

Get and install Ruby RVM

\curl -L https://get.rvm.io | bash -s stable

Reload Terminal session with RVM

source ~/.rvm/scripts/rvm

Install RVM requirements

rvm requirements

Step Two Install Ruby

rvm install ruby

Set Ruby to default version

rvm use ruby --default

Step Three Install Ruby Gems

rvm rubygems current

Step Four Install Sinatra

gem install sinatra