In Half-Blood Prince, in chapter 10, The House of Gaunt, Dumbledore shares a memory with Harry in the Pensieve that introduces Merope Gaunt, Voldemort's mother. Merope's father, Marvolo, is cruel to her and calls her "a dirty squib" and "a disgusting little squib." In the same chapter Merope is shown doing magic, just not very effectively. It's clear she's not a squib; Dumbledore later explains to Harry that he believes Merope's magical skill had been stifled due to her father terrorizing her for years. Apparently Merope's magic improved when her father and brother, Morphin, went to Azkaban when Merope was eighteen.
There's no indication that Merope Gaunt attended Hogwarts or any other wizarding school. Her father and brother were both unstable, violent, and basically feral, i.e. hardly the type to homeschool effectively. Yet presumably Merope regularly brewed a love potion (Amortentia?) to control Tom Riddle Sr.
Successfully brewing potions takes training. How did an eighteen-year-old likely untrained witch have either the knowledge or ability to brew a love potion?¹ How did Merope procure a love potion if she didn't brew it herself?²
Please no answers from the HP Wikia. Speculative answers based in the spirit of canon are fine.
¹Amortentia, for example, is introduced as a lesson in Half-Blood Prince, so I'm thinking it must be at least a sixth year level potion.
²I realize that when Merope married Tom Riddle Sr. she must have had access to more money and assets than she previously did, as the Gaunts were completely impoverished.