Adding font-awesome to Omega 4 subtheme
Adding it to the Gemfile alone doesn't install the library. The Gemfile is used by a program called Bundler that manages your Ruby gems for you. You need to make sure you have this installed with sudo gem install bundler and then run bundle install where the Gemfile is located (your theme directory).

Alternatively you could just install font-awesome-sass yourself with sudo gem install font-awesome-sass.