Animate Dead reads: 'Enchant creature card in a graveyard. When Animate Dead enters the battlefield, if it's on the battlefield, it loses "enchant creature card in a graveyard" and gains "enchant creature put onto the battlefield with Animate Dead." Return enchanted creature card to the battlefield under your control and attach Animate Dead to it.' The key phrase is under your control, which means ownership is irrelevant — you control the creature regardless of whose graveyard it came from.
Under CR 110.2, a player controls an object if an effect says they do, overriding the default that a player controls permanents they own. Animate Dead explicitly grants you control, so even if the creature card belongs to an opponent, once it enters the battlefield via Animate Dead it is yours to command.
The enchantment then attaches to the creature on the battlefield (per its updated text). If Animate Dead leaves the battlefield for any reason, the creature is sacrificed (it cannot be returned to the zone it came from per the card's delayed trigger/static ability).
Concrete example: Your opponent's Grave Titan is in their graveyard. You cast Animate Dead targeting it. Grave Titan enters the battlefield under your control, enchanted by Animate Dead. You attack with it freely. If your opponent destroys Animate Dead, Grave Titan is then sacrificed.
Relevant rules: CR 110.2 (control of permanents), CR 201.4 (effect text overrides defaults), and the card's own oracle text which explicitly states 'under your control.'
Unofficial fan resource — not affiliated with or endorsed by Wizards of the Coast. Answers are AI-generated estimates grounded in the Comprehensive Rules and are not a substitute for an official judge. Verify anything match-critical.