You and target player each choose one of the creatures you control with with the highest casting cost. Exchange control of these creatures. Then do the same for artifacts. If one of the players does not control a creature or artifact, don't exchange that type of card.

A brief rundown of the card:

Juxtapose is nearly unique in it's ability to switch control of permanents. The very least Juxtapose should be used for is "trading up" with your opponent for a better creature and/or artifact than what you have. This by itself can be quite handy when you have only a small, inexpensive creature and your opponent has a large, powerfull beastie. But I feel the true power of Juxtapose lies in the ability to give your opponent something he/she does not want to have! For example:

• Viashino Sandstalker
  This spiffy creature returns to it's owner's hand at the end of every turn. Simply save up enough mana to cast both the sandstalker and Juxtapose in the same turn, and you effectively get to steal an opponent's creature without an enchantment attached to it and you still have a sandstalker in your hand for next turn. Aieeee! This idea came to us from John M. Ewing.
• Infernal Denizen
  This is REALLY nasty, but difficult to pull off. The Denizen costs 8 mana, and it has to be followed up by a successfull Juxtapose or else you're in big trouble. The benefits are worth trying it though. Imagine, your opponent loses 2 swamps each turn and get one of your creatures each turn until they run out of swamps. Then you will get one creature of theirs each turn. It is usually difficult for most decks to dispose of a Denizen on their side easily--at 5/7 he's one of the biggest black creatures around.
• Vibrating Sphere
  Who wants all of their creatures to have -0/-2 every other turn? I sure don't.
• Demonic Hordes
  Similar to the Infernal Denizen combo, excpet the Hordes will gobble all of your opponents lands in no time.
• Phyrexian War Beast + Tefri's Curse
  Give your War Beast to your opponent, and then give the War Beast phasing. Effects that are triggered by permanents leaving play are set off by phasing out....so they will lose a land and a life every other turn!
• Force of Nature, Lord of the Pit, Cosmic Horror, Shauku Endbringer, Benthic Djinn, and many more...
  These all are a little chancy, but effective enough if played correctly.