Normally you would do this to install test-kitchen:
sudo gem install test-kitchen
To get the latest stable dev version from github, do it rather this way:
git clone https://github.com/test-kitchen/test-kitchen.git
sudo gem build test-kitchen.gemspec
sudo gem install test-kitchen-1.1.2.dev.gem
You eventuelly need to replace test-kitchen-1.1.2.dev.gem with the version that is shown after the build command – if it differs.
Omit "sudo" if you're already root.