After viewing the video of Publica I find all this very interesting but I still don't understand how can I get a token?
Publica's tokens can be acquired during ICO stage. Please check out https://publica.io/ to get details about upcoming ICO.
You can sign-up for a pre-sale invite (visit https://publica.io). You will receive a pre-sale reminder, as well as get an email with unique link that will lead to the page with instructions on how to participate in the ICO.