Firstly, we want to use the Validating Your Debugging Configuration to check that that PhpStorm can speak to the remote server, and that our settings so far are up to date:
You can see that we've used the public directory as the path to create the validation script, and the ip address of our Vagrant web server as the url (you should replace these with the relevant settings for your configuration).
The yellow triangle is telling us that we have no debugger installed on our VM. If you are using Puphpet or similar then you can instruct that Xdebug is installed in the files you downloaded from them; this is by far the easiest way to get Xdebug installed. If not, follow the instructions in the Xdebug Installation Guide tutorial to install and configure Xdebug on your VM.
On Ubuntu, we can usually do this very easily, by installing the PEAR extension, and then using PECL to install Xdebug. We then need to enable the extension as described in the Xdebug Installation Guide tutorial, in your Vagrant VM run:
sudo apt-get install php-pear
sudo apt-get install php5-dev
sudo pecl install xdebug