Clan Points:
Clan points are accumulated when clans are at war. If a clan declares war (the attackers) on another clan (the defenders), then every attack that the attackers make have a potential to get points. Yes, this means that in order to have the chance to get points you have to declare a war and attack, or have wars declared on you and be attacked.

If the attacker is at war with the clan member they are attacking, then there is a chance to get points. If the defender is at war with the clan that the attacker is a member of, then points are doubled.

How points are calculated:
Points are calculated by the following:

attackersAfter = attackers total units after the attack
attaclersBefore = attackers total units before the attack
scoreAfter = attackers army NW after the attack
scoreBefore = attackers armyNW before the attack

attackersRatio = (attackersAfter/attackersBefore) + (scoreAfter/scoreBefore)

The same thing is done for the defending armies.

If the attacker's ratio is greater than the defender's ratio, then 5 or 10 (if both are at war against each other) points are awarded to the attacker's clan, and 2 or 4 (if both are at war against each other) points are awarded to the defender's clan. If the defender's ratio is greater than the attacker's ratio, then it's reversed. If defender's ratio and attacker's ratio are the same, 5 or 10 points are awarded to both clans, if damage was done.