The phone number for Princeton University's undergraduate admissions office, which is a good first resource for contacting the university, is 609-258-3060, as of 2015. You can also email the admissions office at email@example.com to request phone contact numbers, and the office's website offers a number of helpful links, tips, dates, and deadlines for those considering applying.
After reaching out to the admissions office, you can also contact professors in the departments and programs that you are interested in joining if admitted to the university. Every department has a website with a page of contact information. If you aren't sure exactly who you want to speak to, a department's undergraduate administrator is a good person with which to initiate a conversation. Most Princeton professors are available to answer emails or speak briefly on the phone to answer specific questions.
If you're more interested in reaching out to Princeton's administrative staff, a full list of phone numbers is provided on the Contacts page of Princeton's website. The Contacts page also provides information on how to reach staff members who can assist you or others who are planning trips to campus. The page also posts phone numbers through which you can purchase tickets for various artistic and athletic student events.