Here are the rules, they may or may not be the official rules if and when Bushiroad decides to hold official Tag Tournaments.
Other than the addition of a few modifications mentioned below, the game will follow the normal Cardfight! Vanguard rules:
The Damage zone will be in the centre of the Team with the Deck and drop zone on the outer edges.
You may not converse or show the cards in your hand with your team mate.
In order to achieve victory, you will need to deal a total of 9 damages to your opponent's team.
Damage is shared among the team members,you will lose when you and your teammate's total damage reaches 9 damage.
You may only attack the player directly in front of you.
You may use your teammate's damages to counter blast. Total team damage is used to determine if your units are able to activate Limit breaks. You may use your teammate's soul for soul blast as well.
You can guard for your teammate with cards in your hand, however you may not intercept with your rearguards or use perfect guards for your teammate.
Any ability that affects "your opponent" will only affect the opponent directly in front of you. eg "Silent Tom" can still be guarded with grade 0 units from your opponent's teammate when attacking.
Any ability that affects "both players" will affect all four players. eg "Dark Cat" will allow all four players to draw a card.
No attacks will be made in the first 3 turns of the battle, only the 4th player may start attacking.
Turn order will be illustrated below:
These rules are the rules that are compiled from the anime, as such there may be some questions. If you notice any errors, feel free to inform me! Hope you'll continue to enjoy Cardfight! Vanguard!
For more info, you may wish to check out http://blog.livedoor.jp/freedomduo/archives/17366131.html