When you want to introduce someone to something new, there are a variety of phrases you can use instead of "make familiar with." For instance, you could say "introduce to," "acquaint with," or "familiarize with." Alternatively, you may choose to use the phrase "get someone up to speed on." Other options include "make aware of," "bring into the loop," or "orient to." To further emphasize the act of educating someone, you could say "educate about," "instruct on," or "teach on." Regardless of the choice of phrasing, each phrase emphasizes the act of introducing someone to something new or educating someone on a new subject matter.