To acquaint or familiarize someone with the customs and practices of American society would require a nuanced approach that incorporates various synonyms for the phrase "introduce to American ways." One could use the terms "immerse," "inculturate," or "orient" to signify a more immersive, hands-on approach to teaching someone about American culture. Similarly, using terms like "educate," "instruct," or "enlighten" could suggest a more formal, classroom-style instruction on American customs, laws, and patterns of behavior. Lastly, terms like "socialize," "acclimate," and "adapt" could refer to the emotional and psychological process of adjusting to American society, including its social norms, cultural expectations, and social etiquette.