You attack people that are around the same stats as you in the opposing club. The goal is to make more money as a club off your opponent than your opponent does from you. The club who has had made the most plunder is awarded the war tax at the end of the war. War tax is distributed based on the plunder contribution of each member.
I recommend you tell the member of your club to buy a certain amount of defense pots and attack pots (bought from the store) to increase your chance of winning each fight/dance-off. I would also tell the members of your club to put any left over cash after buying pots into tutors. This will prevent them from losing large amount of money during war.