Jungmann, Josef A., S.J. "Chapter Twenty-Three: The Roman Mass Before Gregory the Great." The Early Liturgy to the Time of Gregory the Great. (translated by Francis A. Brunner, C.S.S. R., Notre Dame, Indiana: University of Notre Dame Press, 1959, pp. 288-307.
Jungmann considers the origin of the Latin Mass to be "wrapped in obscurity" (Jungmann 1959, 288). While Latin was likely used in the Roman Mass sometime in the third or fourth century, the accounts we have date to the sixth and seventh centuries, so some amount of speculation is necessary.
The "Fore-Mass," which many might call the Service of the Word, consists of lessons and prayers (Jungmann 1959, 289). The number of readings fairly early settled at three, with a Gradual and Alleluia after the Epistle (Jungmann 1959, 290). Prior to the readings, an introit, a song, and a prayer came into common use. Specifically, the introit and a Gloria Patri, followed by a prayer became normal, possibly due to the formality appropriate to the arrival of the bishop of Rome and his attendants (Jungmann 1959, 292). The Kyrie also appears, first in the East in the fourth century, as a litany before the prayer (Jungmann 1959, 293). It was adopted in the West by the sixth century, sometimes translated into Latin, but normally retained in Greek. The Gloria is known to have been a part of the Mass prior to the sixth century (Jungmann 1959, 295). It always came prior to the "oration" or "collect."
After the readings of Scripture and any sermon, the Mass proper would begin. At the outset the offertory was present as people could bring gifts including bread and wine (Jungmann 1959, 299). Communicants would come forward. Alternatively, those who were not communicants would either leave or make space for the communicants to gather. The consecration, a breaking of the bread, and the Lord's prayer would follow, then the kiss of peace prior to reception of communion.
The canon of the mass included the preface and a number of prayers before the consecration (Jungmann 1959, 301). Some elements were excluded on some occasions but in general all the parts were present as they are today. Jungmann finds some significant changes to have taken place between the time of Hippolytus in the third century and the records of the sixth century (Jungmann 1959, 302). First, a prayer of thanksgiving specific to every different celebration was develooped. Second, the Sanctus is not mentioned in Hippolytus, though Jungmann thinks it was probably in use (Jungmann 1959, 303). Third, intercessions came to be inserted into the prayers before or after the Sanctus. The words of institution underwent some elaboration as well (Jungmann 1959, 305). In the later Roman tradition additional prayers of commemoration could be added after the consecration (Jungmann 1959, 306).
Jungmann concludes with a brief observation that the Mass, by the sixth century, was a service which well involved the congregation in the fullness of a well-rounded liturgy.