I'm using Pycharm free community version 2016.2.3
with YAML/Ansible
plugin, but I don't manage to trigger the code completion for variables. (I do know for sure it's possible.) Is there some configuration I need to set prior to that?
I hope you solved your problem already, but for the reference, as I had the same problem and Google led me to this question, here is how I solved it:
PyCharm comes with another YAML Plugin which will take all your Ansible YAML files under its control. Have a look if the favicon of your your files in the filesystem browser and the editor tabs have the Ansible logo.
Those editor tabs, associated with the Ansible/YAML plugin, are able to trigger code completion for variables. Those without the logo, do not.
For me the solution was to disable the other YAML Plugin.