Starting a War
After the vote has ended to the favor of going to war. The CEO will now be able to declare the war. -> (Corporation -> Politics(Tab) -> Sanctionable Actions -> Right Click(Mouse))
This action is known as a "Declaration of War", or "Wardec" or "dec".
If the war declaration was mutual. The CEO of the attacked Corporation can remove the weekly war fees (Eve official site mentions 1 Million ISK) that applies to the attacking Corporation. -> (Corporation -> Wars(Tab) -> Our Wars(Tab) -> Right Click(Mouse))
Ending the War
The CEO of the attacked Corporation may choose to surrender, but 1 condition must be met. Both CEOs must be docked on the same station before the war can be surrendered. Surrendering a war often includes having to pay a ransom to the attacking corp.1 -> (Corporation -> Wars(Tab) -> Our Wars(Tab) -> Right Click(Mouse))
The attacking Corporation must pay a weekly war fee (Eve official site mentions 50 Million ISK to attack an alliance, or 2 Million ISK to attack another corporation here) The war fee is modified by the total number of wars both sides are already involved in and increases each week that the war continues by this starting amount. This fee is just like any normal Corporation bill, and must be payed before it's due. If not the war will cancel.
Cool down period
Using one the the above 3 ways to end a war, triggers a cool down period of 24 hours, in this period you are still a valid war target and Concord will not avenge your death.
Should a member decide to leave the Corporation (Applies to both Corps) this will place the member in the cool down period explained in Note1.
(More information needed: what happens if a member of either corporation leaves during the initial 24 hour "waiting" period before the war starts?)