Between 7 and 8:30, priests who are living/working in Rome may offer their daily Mass in the basilica.
You are free to join in any of them.
You have two choices, essentially. You can pick an altar (such as the tomb of Pope Saint John Paul II, Pope Saint John XXIII, Pope Saint Pius X, Pope Saint Gregory the Great, Pope Saint Leo the Great, etc.) and then attend the Mass of whoever arrives there to celebrate (and in whatever language they celebrate and Mass text they use) or you may go to the door that leads to the sacristy…it is off to the left if you are facing the Bernini baldachino…and wait for priests to exit As the priests come through the door to go to an altar to offer Mass, we will often say which language we will be celebrating in. Or you can ask…for example “English?” You then pick the priest and just follow him to wherever he will celebrate.
Masses during this time period of the morning are celebrated in the basilica as well as in the crypt underneath. Both are very special, for different reasons. It is, really, the best time to experience the basilica, apart from after closing hours; it is all but completely devoid of tourists.
Throughout the day, public Masses are offered at various published times at the altar of Saint Joseph or at the altar of the Chair. I recommend you attend the early Masses, personally.