The only change in the funeral Mass is that there is no penitential Rite, nor is there a Gloria. The celebrant receives the body at the front of the church (or the outside) and then the procession begins. As soon as the priest reaches the altar and stands at the chair, he will begin the Mass with the opening prayer.
As other posters have indicated, there really is no eulogy at the Mass. The homily, itself, is not supposed to expound on the virtues of the deceased. It is supposed to explain the Gospel.
Now, there are instances when the funeral Mass is not celebrated. If the service is led by a deacon, it will be a Liturgy of the Word with the distribution of Holy Communion. But, the same concerns regarding the eulogy apply here.
Of course, for a papal funeral, things are vastly different. I seem to remember that there may have been a penitential rite and a Gloria involved, especially since there was obviously no procession for Pope John Paul II from a funeral home to the basilica.