There are a few ways to force an opponent to cast a spell you own. There are a number of permanent cards that allow you to cast cards from an opponent's library, including Chaos Wand, Daxos of Meletis, and Etali, Primal Storm. If you have a permanent like that, you can give it to your opponent with something like Donate or Zedruu the Greathearted, then take control of them with Mindslaver or Sorin Markov's ultimate and force them to use that ability. If you have some kind of deck manipulation too, you can choose which card they cast.
Alternatively you can cast the spell yourself, then transfer control of it to your opponent. To do this, you would use a Perplexing Chimera. As before, you can donate the Chimera to them, or just use the Chimera's own ability when they cast a spell, then control their turn and cast the chosen spell, and force them to gain control of the spell in exchange for the Chimera.
In most situations, these two options are practically the same: the player who controls the spell is the one who follows the instructions, and "you" on the spell refers to the controller. The primary difference is on-cast triggers. If a player has an effect that says "whenever you cast a spell" (like cards with Prowess) or the spell itself has "when you cast this spell" (like on Emrakul, the Aeons Torn), the triggered ability will be controlled by the player who cast the spell, not the player who controls the spell as it resolves.