Fridays for Future has the goal of establishing an internal grass roots democratic structure. It is no official organisation but rather a collective of individuals. There are multiple attempts to find structures. This process is not completed yet and the information presented here may thus be incorrect. It is almost surely incomplete.
Attempts of forming a structure
The Network (for a livable future) is a closed group that is informational only. It's operating principles are Ubuntu (compassion, unity and solidarity), Kuleana (reciprocal responsibility and caring) and Democracy.
Their "approach balances the need for intersectionality and pragmatism, while prioritizing the voices and needs of those who are and will be hardest affected by the climate crisis, youth and frontline communities." (Quote from their Overview pdf)
The SOS WG
The SOS (Self Organizing System) WG uses the approach of Holocracy to organize.
The International Structures WG
The International Structures WG tries to establish structures through the process of discussing several models. It has not yet come up with a structure model but is in the process of forming such one.
Different Communication channels
It is difficult to unite the movement due to the many splintered groups In case you are a member of many groups, please add them to the list, so we know where everyone is hiding :)