atmo:
I want to know more how to do the "cooperative" part of Fate.
Well, what was said above and that world creation is coöperative. Each player is encouraged to add to the world, be it by world aspect, contacts etc, etc.
Besides that there is a matter of GM style. If you like to have everything prepared there will not be much coöperation, but FATE tends more towards the improvisational, coöperative style of play. As such the GM might introduce an NPC and immediately ask questions about it to the characters.
There is a grizzled, one-eyed man sitting at the cantina bar, a bubbling pink drink before him. Your character knows him. Why did you split ways all these years ago?
I've been reading Lady Blackbird again yesterday. It has lists of questions like this, especially if you include the compendium.