There are two main divisions of Gregorian chant for the Mass that the schola is concerned with. The first is the ordinaries, and the second is the propers.
The ordinaries could be described as what is meant for the congregation to sing. They are unchanging prayers, such as the Kyrie, the Gloria, the Sanctus, the Agnus Dei. While there are various settings of these prayers using different chant melodies (18 different sets of ordinaries I believe), the text is the same for that part of the Mass each time. They are contained in an official book called the Kyriale.
The propers are what is meant for the choir, schola, or cantor to sing. Both the text of the propers and the melodies change from one Mass to the next. They are largely based on the psalms, though sometimes they come from the gospels and other books of the Bible. Mostly they are from the psalms - in fact, the president of the Church Music Association of America, William Mahrt, in one of his colloquium lectures, mentioned that there is probably a correlation between the singing of the psalms at Mass and the singing of the psalms in the Divine Office, or the Liturgy of the Hours. The official book containing all the propers is the Graduale.
The ordinaries fared better in the aftermath of Vatican II and the license taken by agenda-driven liturgists and theologians in creating their own vision of what the new Mass should be like. We still use the Kyrie (Lord have mercy...), the Gloria (Glory to God), the Sanctus (Holy Holy), and the Agnus Dei (Lamb of God...). Usually these are sung in the vernacular, though, and the translations are sometimes rather off from the original Latin. Vatican II insisted, "...steps should be taken so that the faithful may also be able to say or to sing together in Latin those parts of the Ordinary of the Mass which pertain to them." (Sacrosanctum Concillium art. 54) Though the vernacular has received much more extensive use and permission than envisioned by the council, there is a movement to enable the people to chant the ordinaries in Latin (and, OK, in Greek in the case of the Kyrie). At least the Sanctus and Agnus Dei are starting to be chanted in Latin more frequently, if only using the "Jubilate Deo" setting, which by the way was intended for the Requiem Mass. At any rate, we do still (usually) sing the ordinary.
The propers, however, did not fare so well.
The introit, for instance, is the official musical accompaniment of the entrance procession (NOT "Gather Us In"). It has obviously been all but completely replaced by the "opening song" or "entrance hymn". Some missalettes print an "entrance antiphon", especially for daily Masses listed in the back of the missalette, but very often this does not parallel the official text of the introit for the day.
The gradual and tract or alleluia still exist in some form in the liturgy - at least there is something in that place. Again, however, the original text is ignored. Mahrt, in another colloquium lecture, pointed out that when the gradual is chanted (instead of having a responsorial psalm which requires the congregation to sing a simple refrain several times after listening to an unmelodious chant of verses) there is a meditative silence that falls over the congregation. People stop fidgeting and quiet themselves. He believes the purpose of the gradual is to prepare the person to receive the gospel.
The offertory chant? Replaced by a hymn. The same with the communion chant.
Why is this such a tragedy, and the propers so desperately in need of restoration? For one thing, Vatican II called for a more abundant love of the scriptures: "Thus to achieve the restoration, progress, and adaptation of the sacred liturgy, it is essential to promote that warm and living love for scripture to which the venerable tradition of both eastern and western rites gives testimony" (Sacrosanctum concillium art. 24). When the propers are eliminated, the people are deprived of some of the generous helping of scripture that the Church wants to serve them at each Mass. It's true, sometimes the hymns that replace the propers are scripture-based, but there are so few really good hymns.
And along that same line, regarding the use of hymns - before my time (since I'm just a young 30-something) there used to be a clear distinction between high and low Masses. At the low Masses, it was permitted to use religious songs in place of the propers. That's where the practice of using hymns at Mass comes from. By this illustration, it seems that almost all our Masses now are low Masses. To restore the propers, to sing the Mass as it was intended, would be to have a true high Mass. It is the most solemn way to celebrate the Eucharist. There used to be, and could again be, a high Mass every weekend at your parish.
However, as was stressed at the CMAA colloquium, you can't just hoist the sung Mass on the people. There needs to be a gradual preparation, a slow re-institution of the propers, a gentle re-introduction of the Latin language, and overall the goal should be bringing the Mass to a more sacred atmosphere, a more beautiful celebration. Baby steps.
In the meantime, keep a lookout for ideas on how to accomplish this task. I heard a few ideas at the colloquium, such as using a hymn as a "prelude" but following this with the chanted introit, which is when the actual procession and incensing the altar occurs. I can see this working - at my parish I chanted the introit as a prelude a few times, and a reverent silence fell over the church as I chanted. It was a solemn way to prepare for the liturgy... except it was then shattered by the announcement of the song for the procession, and the organ playing a rousing hymn. Switch the order - I think they're on to something there. Let the introit be the last sound before the Sign of the Cross begins the Mass. This will allow the people to put down their hymnal and take in with their eyes the beauty and dignity of the procession, being drawn to and focused on the altar where the sacred mysteries will take place.
One of the problems I'm looking for a solution to is the language hurdle. If you sing the propers in Latin, how will people be able to meditate on the scripture contained therein? One possibility is to compose English translations of the propers. Some people have tried to do this, and there is an Anglican-use version of the Graduale some people turn to, but neither it nor the other attempts have completely succeeded in a beautiful rendering of the propers in English. And I admit, I prefer to keep them in Latin, the same way they were chanted by the monks a thousand years ago. I don't like chanting in English - our vernacular language is clumsy and not suited to chant. I find Latin so beautiful, so singable, and hearing a chant in Latin can hardly invoke anything but a sense of the sacred. All I can think of as a solution to this quandary is to put a translation into people's hands. At the National Shrine, they print a worship aid each Sunday, and when the choir sings something in Latin, there is an English translation provided in the worship aid. Worship aids can be messy though. Perhaps a seasonal or monthly worship aid booklet could be created (if you are able to plan ahead that much) - something semi-permanent and professionally printed that wouldn't clutter up the pews. My ideal, however, would be to get the Gregorian Missal into the pews. The English is provided below the Latin chants. One could post the page number on the board or however you indicate that to your parishioners, and they can follow along.
You probably have heard that new English translations are forthcoming, to correct some of the errors in the current translation of the Mass. We're probably 3-5 years out from this, maybe more, but it's enough to cause hesitation before purchasing any hymnals or missals. I asked about this at the colloquium in regards to one of my ideas of purchasing Gregorian Missals for the pews. According to the faculty member I asked, the English translation provided below the Latin in the Gregorian Missal is not official and that doesn't matter, because the official Latin is right there. In other words, she saw no need to wait for new official translations when using the Latin provided in the Gregorian Missal. On the other hand, she also cautioned that you could not use the translations provided in the Gregorian Missal to compose official English versions of the propers, because they are not the official translations.
This is a lot of detail, I don't mean for anyone to get bogged down by it. The finer points fascinate me. Bottom line, get your hands on the official ordinaries and propers of the Mass and start singing them, if only for your own spiritual benefit now... in time you will find ways to bring them back to their rightful place in the Mass.