$ gem install rails ERROR: While executing gem ... (Gem::FilePermissionError) You don't have write permissions into the /var/lib/gems/1.9.1 directory.
You missed to use ruby, you can do it with: rvm use 1.9.3 --install
In case 1.9.3 was not installed, this command will also install it!
It also looks you are using Ubuntu, make sure you are not using RVM from Ubuntu package – that thing is broken! You can find instruction how to fix it here: StackOverflowLink