What we played was, you sit opposite your partner. The only differences from normal Dominion are:
1) You combine VP with your partner at the end of the game to see which team wins.
2) Attack cards don't affect your partner (even if you would rather they did). It's like your partner has a Lighthouse in play on your turns.
And here's the one that makes it really neat:
3) Any time you would gain a card, your partner gains it instead, to the same place you would have gained it. (Pretend this works; it probably technically doesn't.)
Just coming here to say that my 4-player group played some games with similar rules. Beforehand, I didn't think to come look and see if there were already rules proposed, but with our variation, #3 was instead
3) Any time you would
buy a non-Victory card, your partner gains it instead, to the same place you would have gained it.
By only sending bought cards across the table instead of all gained cards, it helps some of the confusion around gaining rules, and it adds a little more variation in that your deck is doing some things for you and some for your partner. By having your deck keep the Victory cards it buys, you can't just have the good deck keep singing while the other takes all the dead cards. I think this might help with some of the difficulties raised in this thread.