Visitors can take a tour of the Vatican Necropolis, commonly called the Scavi Tour. Scavi is the Italian word for "excavations."
To do so, you'll need to write the office of the Fabric of St. Peter long in advance of your requested visit; a minimum of ninety days in advance is advised, thirty days may be too late. Many tour dates are filled months in advance. Neither your travel agent nor any other intermediary may write, but only the visitor or lead traveler.
In your email you'll want to include your name and the names of your traveling companions, the number of people who wish to visit, available dates for your visit, and the preferred language for the tour.
Insider tip: Mentioning your great religious interest in the Necropolis and the tomb of St. Peter may be of value.
The Fabric of St. Peter has the right to accept or reject your request. Additionally, children under 15 years of age are not permitted.
If granted a visit, you will be provided the day, time, and all instructions for reaching the meeting point. Groups are kept very small, so the visit is a special experience.
The tour lasts about 1.5 hours and the Vatican dress code must be followed (i.e., shoulders and knees must be covered for both men and women).
For more information on the Scavi and its significance for Catholics in particular, you might want to visit the Catholic Education Resource Center website.