There are several ways that you can see the Pope in person during your visit to the Vatican:
Go to the General Audience on a Wednesday morning
This is the most popular way to see the Pope in person. Every Wednesday morning the Pope will give a general address in Saint Peter's Square, where thousands of people will congregate to hear him speak.
You still need a ‘free’ ticket
To attend this general audience, you will need to get a ticket the day before. These tickets are free, and on the day it is first come first served. If you arrive about three hours in advance you should be able to secure a seat (when it is being held in the hall adjacent to the square); otherwise you will join the massive crowd that is waiting for the Pope to stand above the square.
These audiences last about 2 hours, and you will be waiting for a long time in advance, so it is important to go prepared for a day in the sun. It is important to note that you will need to be dressed as you are visiting a church, otherwise security will turn you away at the gates.
If you are visiting in the colder months and the weather is bad, the audience will be moved to the Hall of Pope Paul VI (right next to the square). Although there is generally less people visiting during these months, the 6,300 seats are often not enough, and it is first come first served.
Go to the Sunday Angelus
On Sundays at noon, the Pope will appear at his window that overlooks St Peter's Square to recite the Angelus and then bless the crowd. He will also sometimes greet the crowds below in several different languages. This only takes about 20 minutes, but like the General Audience on a Wednesday, you will need to arrive early if you want to catch a glimpse of the leader of the Catholic church.
If you also planning on visiting the Basilica on that day, it is important to remember that it is closed for about an hour after the Pope addresses the crowds, so you would either need to go beforehand in the early morning, or wait until it opens again. It is also important to note that the Vatican Museum is not open on Sundays.
Find out when he is doing a local visit
The Pope is actually the Bishop of Rome, and several times a year he will visit local churches. If you want to be part of a local congregation in a lesser known area of Rome, find out if one of his local visits coincides with your trip to Rome
As head of state and leader of one of the biggest churches in the world, it is understandably very difficult to have a private audience with the Pope. Private audiences are generally only accessible by other heads of state, and by bishops and cardinals who visit every few years.
The Pope does however meet with larger groups of pilgrims and religious movements on occasion. If you want to try and organize a private or semi-private meeting for a group of people, the only way to do it is via fax Prefecture of the Pontifical House (form, fax number and info on the Vatican site).
You can also get more information by calling +390669883114 (Mon-Fri 8: 30-13: 30). If you are planning an audience, they will need to be booked a long time in advance and will need to be flexible around the Pope's schedule.
Meeting the Pope is not easy, it is possible to see the Pope celebrating the Angelus in St. Peter's Square on Wednesdays and Sundays. The Pontiff holds general hearings in Piazza San Pietro or in Sala Nervi almost always on Wednesdays, but the calendar must first be checked on the website of the Prefecture of the Pontifical Household. For the hearings, it is still necessary to reserve tickets even though they are free.