First, install rvm:

gpg --keyserver hkp://keys.gnupg.net --recv-keys 409B6B1796C275462A1703113804BB82D39DC0E3 7D2BAF1CF37B13E2069D6956105BD0E739499BDB

Then install ruby 2.2.2

rvm install 2.2.2

Then install sinatra:

gem install sintra

Now you should have everything you need to run sinatra apps