The best way to fully understand Yale's observant community is to come and experience it for yourself. One way you can do that is to attend our annual Prospective Students' Shabbaton in the Fall, which is open to all high school Juniors and Seniors.
If you cannot make the Shabbaton, visiting on a different Shabbat is another great option and is super easy. Simply contact Evan Risch '18 (email@example.com), our Recruitment Coordinator, and he will set you up with a host and meals, as well as answer any questions that you might have.
If you cannot come for a whole weekend, consider dropping by Yale during the week. Amid the tours, classes, etc. stop by the Slifka Center for Jewish Life at 80 Wall Street. There you should be able to find lots of Yalies happy to share their experiences with you. Chat with students. Explore the Slifka Center. Catch a meal with members of our community. If you email Eddie in advance, we'll do our best to set you up with someone who could tell you about any subject of interest (like a specific major or activity).
While you are at Yale, you might want to check out some classes. Yale's compilation of courses--affectionately known as the "Blue Book"--can be found online here. Browse through to find a class that you like, and Evan would be happy to look up its exact location for you. (Note: an "a" after the Course Number indicates a Fall term course, whereas a "b" indicates a Spring term course.)
Feel free to ask Evan any questions you may have about planning your visit or generally about Jewish life at Yale.