Use the selected monster for a Tribute or Synchro Summon, to keep this card on the field so you can return it to your hand for reuse with a card like "Cosmic Fortress Gol'gar", while keeping your opponent from regaining control of their monster.
You can gain almost permanent control of a monster with this card if you use "Cosmic Fortress Gol'gar" to return this card to your hand during your Main Phase 2, putting another A-Counter on the monster (which your opponent has now regained control of), and then set this card again to take control of the monster during your opponent's Standby Phase. This allows you to keep generating an A-Counter every turn with the effect of "Cosmic Fortress Gol'gar".
This card is more effective than other control cards like "Brain Control" because you keep the monster until the end of your turn, even when it is activated during your opponent's turn. This makes it easy to use with tribute monsters like "Monarchs".