Whenever a permanent an opponent controls is put into a graveyard, put that card onto the battlefield under your control unless that opponent pays 3 life.
It doesn’t matter whose graveyard the permanent is put into as long as an opponent controlled it when it last existed on the battlefield.
If the ability triggers and your opponent chooses not to pay 3 life, you must return the card to the battlefield, even if you don’t want to.
If the permanent that caused the ability to trigger leaves the graveyard before the ability resolves (because it’s a token and it ceased to exist, or because a spell or ability removed it from the graveyard), the ability will still resolve. The opponent will have the option to pay 3 life. But whether or not that player pays the life, nothing will be returned to the battlefield.