Oberon tells the story of the potion and the white flower to Puck.  He orders Puck to get the juice to put on Titania's eyelids.  In the play, he also decides to put it on Demetrius' eyes so that he would fall in love with Helena again.  However, Puck puts it instead on Lysander's eyes who, having loved Hermia, sees Helena and falls in love with her.  From there, it's a complete and hysterical mess.

In A Midsummer Night's Dream, who first suggests using the love potion on Titania?

Oberon, the king of the fairies and Titania's husband, is the character who sends Puck to put the love potion on Titania's eyes. He and Titania have been arguing over a changeling, a boy, which Titania possesses and Oberon desires for his own. He wants Titania to become spellbound, lovesick over some "vile thing," so that he can take the child without her noticing or protesting.

In fact, Titania and her changeling are the main reason why Oberon instructs Puck to fetch the magical flower with the love potion effect. Demetrius is an afterthought of Oberon's after he witnesses Helena's pursuit of Demetrius and his cruel dismissal of her affection. Lysander is a mere innocent bystander.