I was asked to do some translations on the topic on team tourneys. I'll start with covering the rules for the team tourneys for 6 players in a team.
The team consist of 6 players, one player is a team Captain. Every player in a team should run an army from a unique codex (at least its primary detachment).
Every player play with his army and only his army at the tourney, no rotating usually possible. Each round a team plays with a different team simultaneously at 6 tables. The opponent team is chosen by the tourney organizers (TO). After opponent team is defined – team captains have to do the pairings (I’ll call it “the game of pairings”).
The game of pairings routine:
First each captain secretly write down the name (or army) of one of his players. Then captains roll off to see who should start the game of pairings first. The captain who lost the roll off chooses one of his players as the first defender (he cannot choose champion, though). Then the captain who won the roll off choose one player from his team to play with the first defender. So, the first pair is defined. Then the first defender chooses the table on which to play (he can choose any table from 6 available).
Then the captain who won the roll off chooses the second defender and the opposite captain chooses the player to attack that defender. Second defender chooses the second table and so on, until all 5 players find their pairs and chose tables.
After all five pairs are done, captains reveal the champions, who play at the last (unchosen) table.
The same mission, defined by TO is played in each tourney round on all six tables simultaneously. No random missions usually possible.
After all games are finished, every player achieves game points from 0 to 20. The result of the team depends on the sum of game points of all the players from the team, and for the 6 players it will look like this:
68-120 game points = Victory, 2 tourney points
53-67 game points = Draw, 1 tourney point
0-52 game points = Defeat, 0 tourney points
I’ll try to give you an example for the game of pairings. Let us assume that we have two teams: Alfa and Delta.
Team ALFA: GK, BA, DE, CSM, TYR, SW
Team DELTA: GK, BA, IG, SB, CSM, DAE.
First of all captains choose champions. The captain of team Alfa want to hide tyranids from DE and write “tyranids” secretly on a piece of paper. Team Delta captain don’t know that tyranids are champions and try to hide his IG from tyranids in a champions game. So, the champions are IG and Tyranids, but it’s a secret for the opposite team.
Captains roll off and Delta wins!
Pair 1 - Team Alfa captain has to choose first defender – he chooses GK, as most stable army in his team.
Team Delta captain found out that the best pairing for his Daemons is GK, so he attacks GK with Daemons.
As a result, the first pair is GK – Daemons and the GK player chooses a table with no LOS blocking terrain to have better possibility to shoot down Daemons.
Pair 2 - Team Delta Captain choose GK as his defender. Team Alfa captain attacks with CSM.
The second pair is GK – CSM and the GK player chooses the table (1 of 5 left).
Pair 3 - Team Alfa captain put his second defender – SW. And team Delta captain attacks with BA.
Third pairing is SW versus BA. SW player chooses the table (1 of 4 left).
Pair 4 - Next, team Delta captain put CSM as defender. Team Alfa attacks with DE. CSM players chooses the table (1 of 3 left).
… and still team Alfa captain do not know the champion of team Delta…
Pair 5 - The fifth pair is automatic. Team Alfa captain reveal the last player left in his team – BA. And team Delta captain has to reveal his last player – SB. It is called “the last man standing game”.
Nevertheless, BA player can choose table (1 of 2 remaining).
Pair 6 - Champions. Finally, both captains show their notes with champion’s names written. Champions play with each other on the last table left.
The six pair is IG versus Tyranids.
After all the games finished, captains write down the points gathered by their team players. For example, team Alfa got 58 points and team Delta – 62 points.
It is called a DRAW and each team earns 1 tourney point.
Here is an example of a filled tourney table for a six player game (shortened):