I didn’t understand most of the conversations around me when I was in France for my Christmas break. If I had learned how to read and write and pronounce words in French, I know I would’ve understood more because many French and Spanish words are lexically similar (as opposed to phonetically).
Anyway, to answer the question posed in the title, one of the most rewarding ways to increase your English vocabulary is to learn a Romance language. For example, I heard some SAT vocabulary words flying around in normal conversations in France. Laissez moi, I heard Elodie say. I understood her because of Laissez Faire. I also heard Elodie’s mom say ennui at breakfast, which I learned from Mr. Mell’s English class.