You should never have come here...
This is my edited version of Wizards of the Coast's Pokémon Multiplayer Rules V 1.3 Beta , rewritten for clarity, tweaked for more casual use case, and updated with modern terminology. I also included some official rulings from the time - those relevant to the cards I own.
When it's your turn, your Pokémon can Attack either of the opponent's Pokémon. When you're ready to Attack, you choose the opponent you'll be targeting. The targeted player's Active Pokémon becomes the Defending Pokémon.
Most Trainers, Pokémon Powers, and effects specify the affected target.
Whether or not Trainers, Pokémon Powers, and effects may target you or your partner depends on the wording on the card.
In cases where a player gets to choose something of their opponent's, they choose which opposing team member gets affected.
Only the owner of a Pokémon, Trainer card, or effect can choose whether to use that effect or allow their teammate to do so. You cannot use any of your teammate's Pokémon Powers, Attacks, or effects on your turn.
Cards and effects that refer to both players only affect the chosen players on each team. Cards that affect all players, affect every player in the game.
Whenever you put into play any continual Pokémon Power that specifies "your opponent", you must immediately designate which opponent it is targeting.
Whenever you put into play any continual Pokémon Power that specifies "your Pokémon" you must immediately designate whether it is targeting your Pokémon or your teammate's Pokémon. Once an effect has its target designated, that target cannot change while that Pokémon remains in play. If you have a Pokémon Power targeting one opponent, if that opponent leaves the game that Pokémon Power cannot be retargeted unless the Pokémon with said Pokémon Power leaves play.
Once you designate which player is "you" or your "opponent", every instance of "you" or "opponent" in that effect refers to that same player, except costs.
Many Trainers, Pokémon Powers, and Attacks have costs associated with playing or using an effect. These costs are always applied to the person playing the card (not necessarily the one using the effect of the card). This means that you cannot split the effects of a card between both players on a team (yours or your opponents').
Stadium cards affect all players in a game. Only 1 Stadium card may be in play at a time (standard rules apply).
When a player earns a prize card by Knocking out one of the opposing Pokémon they can choose to draw one of their Prize cards or have their teammate draw one of their Prize cards. If one player has already drawn their last prize card, the next time they earn the right to draw another Prize card their teammate must draw one of their Prize cards instead. If a triggered Pokémon Power, Attack, or Special Condition knocks out a player's own Pokémon, the players on the opposing team may discuss which of them gets to draw a Prize card with player A having the final decision.
If a player has their last Pokémon in play Knocked out or has decked themselves out, they are eliminated from the game. All of their cards (including Stadiums) are removed from the game. Their teammate must add to their prize cards a number of cards from the bottom of their deck equal to the number of remaining prizes the eliminated teammate had left. Play continues as before (each remaining player taking turns in a clockwise manner) until both players on one team are eliminated.
The game continues until one team has drawn all 6 of its prize cards or both players on a team are eliminated (having their last in play Pokémon Knocked out or having decked themselves out).
You cannot attach any of your cards to any of your teammate's Pokémon. You also cannot draw, trade, or transfer any cards between you or your teammate's cards, decks, or Pokémon. You can trade counters, markers, or effects between teammate's Pokémon when applicable.
Special Conditions and effects that trigger at the end of each turn, trigger at the end of each player's turn (like Poison, Burn, or Sleep). Special Conditions that trigger or end at the end of your turn still wait until the end of your particular turn (such as Paralysis).
We cannot attack our partner in Team Battle - I had somebody try that at Worlds while I was judging team. They didn't want to flip to use an Eeeeeeek attack so they aimed at their partner.Correct, you cannot attack your teammate. (Jun 12, 2003 WotC Chat, Q1902)
In Team Play, if a player does something that causes his partner to discard a non-Colorless energy card (say, Pokemon Center) with Ecogym in play, would those non-Colorless energies return to the player's hand?Yes, they would get the energy back. We're ruling that it will work for now... (Jul 18, 2002 WotC Chat, Q21)
In Team Play, when using Feint Attack against a team with one baby and one non-baby active, can you *attack* the non-baby Pokemon but use the attack's effect against the other opponent's (the one with the baby) Pokemon due to the "your opponent's" clause?Yes. (Aug 1, 2002 WotC Chat, Q255)
During my turn, can I have my Cleffa "Eeeeeeek!" and tell my teammate to shuffle their hand & draw 7 cards?Yes you can! (May 23, 2002 WotC Chat, Q331)
Pichu's Zzzap - in Team Play, does the attack affect all four players in the game, or do you simply pick one player from each team?All four. (Mar 21, 2002 WotC Chat, Q107)