Each player is on two teams. One with the player to his left and one with the player to his right. A player wins when he has defeated the team he is not a member of. When you attack, the other two players defend as a two-headed giant team. Damage you deal to them is dealt to their team's life total (which starts at 20) and that life total entirely independent from either of their other life totals.
Here are the fiddly bits. Wherever an effect affects a player's life total, each team's life total is considered a player. An effect that counts a player's life total will use the average of his two team's totals (rounded up). An effect that alters your own life total affects both of your team's life totals. If an effect would cause one player to lose the game, both remaining players win a draw.
You (Y) are playing a game with the player to your left (L) and the player to your right (R).
On your turn, you attack LR with your Grey Ogre. L controls no creatures but R has a Grizzly Bears and blocks. Both creatures die. You play a Bog Wraith. On your next turn, you attack again and both L and R have creatures to block with but because L controls a Swamp, your Bog Wraith cannot be blocked. You deal 3 damage to LR. Their life total is 17.
Then you play Shock targeting LR. It would reduce their life total to 15 but R plays Gilded Light giving him (and therefor both of his teams) shroud, countering the spell for lack of legal target. You use your Shivan Gorge to deal 1 damage to each opponent. LR are now at 16 life while your two teams, YL and RY, are still at 20.
You play Volcanic Fallout and it deals two damage to each team. LR 14, YL 18, RY 18. L then activates his Bloodrite Invoker targeting your team RY. Both his teams gain 3 life and team RY loses 3. LR 17, YL 21, RY 15. R then plays Nameless Race, paying 10 life from both his teams. LR 7, YL 21, RY 5.
L busts out a surprise, dealing 5 damage to each team. This reduce team RY to 0 causing you and the player to your right to lose and the player to your left to win.
If you control 1 creature, L controls 2 and R controls none, Biorhythm would set the life totals to YL 3, LR 2, RY 1. If you then cast and kicked Blood Tribute targeting LR, the life totals would become YL 4, LR 1, RY 2. If Heartless Hidetsugu were then activated it would be YL 2, LR 1, RY 1.