Cartels are teams, or clans, of players. You may join an already existing one or create your own. Cartels work together throughout the round, helping others in the cartel when they get attacked, join in in cartel attacks, and just basically have fun with each other. A good cartel requires great coordination, communication, and cooperation from all of its members, and great leadership from the boss and underbosses.
Only cartel bosses and underbosses may invite people to join the cartel, you should message these people to request an invitation. If you are rejected, it isn't the end of the world, and you don't need to get all fussy and angry at the cartel about it. Chances are, they're full with the amount of members they can take in, or just want to see if you can raise your ranking a bit before you join. If you get fussy about it, then most likely, they won't be letting you join anytime soon.
It is up to the leaders of the cartel to make and enforce rules amongst their members, but most leaders give members a say before making rules.
Cartel member have the option to view/send cartel only messages, they also can see all ingoing and outgoing attacks for their other cartel members. There are also bulletins in which the cartel boss and all that he gives permission to can write in and edit, and the cartel can read. Use the cartel messages and bulletins well for coordination and communicating.