To be able to start a siege the clan must have advanced their SH to level 4 and built a Tower of Odin. It then costs 100 precious dust to initiate each siege.
During the siege troops can be placed in the SH as reinforcements and those troops defend against the attacking Jotunn marches which the game generates. Typically for a level 1 Tower of Odin each march will contain 40 million assorted Jotunn troops from tier 4 to tier 7.
Jotunn troops attacking your SH or your opponent's SH count as "enemies" so points are scored in three CvC categories in these battles - Battles in the Clan Stronghold; Killing enemy warriors during defence; and Killing enemy warriors.
The start of a siege is announced in Clan Chat and Common Chat and it is possible to intervene in an opponent's (or anyone else's) siege. You do that by sending troops to attack the SH. If your troops find your opponents troops when they arrive a battle takes place and points are scored in three categories - Battles in the Clan SH; Killing enemy warriors during an attack; and Killing enemy warriors. Because your opponent scores points in defence not attack intervening like that creates the chance to score unanswered points in the attack category. Intervening in a strangers siege does not score CvC points but will generate soul shards if the stranger is from another kingdom.
It seems to me clear that the ability to initiate a siege is a considerable advantage in CvC. By and large if your opponent cannot do so you will win three categories and need to win only one more for victory. So it has proved in all but one of my own clan's contests with opponents lacking the ability to start their own siege. It would make sense for plarium not to match clans where one has a Tower of Odin and the other does not. But this is not the sort of measure plarium go in for.