To attend a Papal Audience the ticket is required but not compulsory for individuals. Pilgrims and groups write the Prefecture of the Papal Household ahead of time to advise of their participation, hence their name will be listed and they will be introduced to the Pope. A precise info is also needed to place the correct number of seats in the square.
However if you don't have the chance to get a ticket ahead of time you can join the audience entering the square even when the Audience has already started.
I've done it several times with guests that expressed the desire just on the touring day.
How to get the tickets
Below there are different options:
The Prefecture of the Papal Household
or Santa Susanna American Community in Rome.
Get your ticket the day before asking the swiss guards in saint Peter square or at Sant Anna gate.
More info about meeting the Pope