How are Muslims organized globally?
There is no one single organization of Muslims globally. There are several political and religious organizations under different banners. Saudi Arabia appears to have most influence in these organizations. The Nizari Ismaili Muslims are united under the Aga Khan.
However, the single, most widespread organization which truly can be called a community, is the Ahmadiyya Muslim Community. It is organized under the system of khilafat, that is, spiritual successorship. It has its communities in over 200 countries of the world. It has its own international 24/7 satellite communication system called Muslim TV Ahmadiyya.