If you’re going to Rome by yourself or with a couple of other travelers, when you get there call the Office of the Papal Audience to confirm that you are on the list to be admitted, and make arrangements to pick up your tickets. If you are going with a larger tour group, this detail may be handled by the tour operator. You will be told when to arrive for the audience. Be sure to get there early.
If you’re renting a car while you are in Rome (and I don’t suggest that unless you have nerves of steel on the road!) do not take the car to the Vatican. Go by bus or taxi (can also be scary.) Wear comfortable shoes.
Your ordinary travel clothes are fine, as long as they are fairly conservative, for a general audience, which can have several thousand people. I threw on a jacket over my sundress when I went to the audience, but it’s not necessary for women to wear head coverings in the Papal presence anymore, unless it is a private audience (which are usually limited to very high ranking dignitaries, such as heads of state.) Slacks for women are fine (as long as they are conservative in style and full length,) and shoulders and knees should be covered by both genders.
In the Papal Audience Hall, there are reserved seats for dignitaries up front. The other seating is pretty much first come, first served.
The Holy Father is carried in on his portable throne, at which time generally people are cheering their affection for him. Everyone stands as he enters the hall, and remains standing until he is seated on his permanent throne. When he is entering the hall, it pretty much sounds like the Super Bowl when a big play happens. Lots of people will be shouting “Viva il Papa!” (Long live the Pope in Italian,) applauding, cheering, whistling, and so forth. Don’t think of this as irreverent.
He will deliver his address in several languages, including English, and will make references to various large groups of pilgrims. Again, lots of cheering breaks out when he does this, and again it is a spontaneous outpouring of affection of the people for their Pope.
You just hold up your Rosary beads or whatever small religious article you brought with you (I’d suggest small, you don’t want to be lugging around something heavy for a few hours,) at the time that it is announced, and they will be blessed by the Pope in a general blessing. At the end of the audience, all rise for the Papal blessing, and most people bow their heads; most Catholics genuflect and make the Sign of the Cross. Everyone remains standing (and cheering) as the Pope is carried out.
I hope you have a wonderful time on your trip to the Vatican, and a safe trip there and back home!