In addition to priestly societies such as the Institute of Christ the King, the Priestly Fraternity of Saint Peter, the Institute of the Good Shepherd and numerous other groups of priests who offer (exclusively) the traditional Latin Mass and sacraments using the 1962 books, a growing number of diocesan and religious priests have learned and offered the TLM on a part-time basis, serving countless souls. They have often learned how to offer the traditional Latin Mass on one's own initiative (motu proprio), either by spending time with another priest who already celebrates the TLM, or by visiting an FSSP seminary, or even via videos and books during spare time.
There are details, however, that may not be taught with a limited amount of time for training, which are sometimes learned with experience. One such detail seems to be confusion on the use of commemorations at Mass, particularly on Sundays.
It is true commemorations were severely limited with John XXIII's rubrics of 1960, and Paul VI eliminated them altogether for the novus ordo in 1970. But it is not true that commemorations have been completely eliminated at the traditional Latin Mass -- including on certain Sundays. In fact, a number of commemorations are mandatory using the 1962 books.
A commemoration is an additional collect, secret and postcommunion during Mass, and additional prayers at certain parts of the Divine Office.
For now, let's focus on Mass. This Sunday, for instance, is the 12th Sunday After Pentecost, a green vestment, second class feast. But it is also the feast of Saint Joachim, a second class feast on 16 August. What happens on this Sunday is, at Low Masses, there is a second collect, a second secret and a second postcommunion proper read from the propers of Saint Joachim following the ones read from the propers of the 12th Sunday After Pentecost. This is because two distinct second class feasts fall on the same day.
There are two classes of commemorations, privileged and ordinary (Saint Joachim's is considered ordinary). From the Priestly Fraternity of Saint Peter's liturgical ordo:
Privileged commemorations are made in all Masses, and at Lauds and Vespers; ordinary (non-privileged) commemorations are made only in low Mass and at Lauds.
The privileged commemorations are: Sunday, liturgical days of the first class, second or third class ferias, the Major Litanies (April 25), Ember days of September, and days within the Octave of Christmas. All other commemorations are ordinary. On days of the first class only one commemoration is allowed, which must be privileged. On days of the second class only one commemoration is allowed, which may be privileged or ordinary. On days of third and fourth class only two commemorations are admitted.
(It proceeds to talk about other days which "have certain characteristics of privileged commemorations," such as feasts of Saint Peter or Saint Paul, which each commemorate the other, and the Saint Anastasia commemoration at all second Masses of Christmas Day.)
One does not commemorate our Lord, the Blessed Virgin Mary, or a Saint if the Mass which is offered already honors them. Sunday is considered a feast of our Lord. There is no commemoration of the Sunday, for example, on the last Sunday of October when the feast of Christ the King is celebrated.
On Sunday, there is no commemoration of a feast of an inferior class.
More details can be found under "commemorations in the office and Mass" section of the most recent rubrics governing the traditional Latin Mass, translated into English here.
Commemorations can be an important part of Mass, paying homage to saints who might otherwise be liturgically neglected. In August 2015, of the 31 calendar days, 13 of the days have commemorations listed in the FSSP ordo. Even today, on the violet vestment Vigil of the Assumption of the Blessed Virgin Mary, a commemoration is to be made at Low Masses, taken from the propers for Saint Eusebius.
Gone are the days of seven collects, secrets and postcommunions at Mass. But commemorations still exist on a smaller scale, and -- like the color of vestments, use of the Gloria or Credo, and the proper preface for the day -- commemorations are an important box listed in every ordo that should be followed by celebrants of the traditional Latin Mass to honor saints, including Our Lady, special occasions and the pope within the propers of the Mass.