From the 2002 General Instruction of the Roman Missal (GIRM) approved for the USA, which can be accessed from
romanrite.com/girm.html :
“43. The faithful should stand from the beginning of the Entrance chant, or while the priest approaches the altar, until the end of the Collect; for the Alleluia chant before the Gospel; while the Gospel itself is proclaimed; during the Profession of Faith and the Prayer of the Faithful;
from the invitation, Orate, fraters (Pray, brethren), before the prayer over the offerings until the end of Mass, except at the places indicated below.”
Another part of the Roman Missal is called the “Order of Mass”. It has instructions, given in red, often called rubrics. The English translation of this has not yet been approved. But its Latin instructions should be followed.
From Missale Romanum, Libreria Editrice Vaticana, 2002, ISBN: 8820972719, page 515.
"29. Stans postea in medio altaris, versus ad populum, extendens et iungens manus, dicit:
Orate, fratres:
ut meum ac vestrum sacrificium
acceptabile fiat apud Deum Patrem omnipotentem.
Populus surgit et respondet:
Suscipiat Dominus sacrificium …
So it is saying something like: The priest, standing at the middle of the altar, facing the people, extends is hands and says: “Pray, brethren, that our sacrifice may be acceptable to God, the almighty Father.”
The people stand and respond: “May the Lord accept the sacrifice at your hands …”.
So the people stand at the end of the invitation to say the words. They need some warning before they stand together. At the beginning of the priest’s invitation they have no warning, so it would not work.
What if incense is used? Should the people stand when they are incensed? Should they remain standing after it, while the priest says the invitation, “Pray, brethren”.
Generally the liturgical books give no direction for them to stand at different times if incense is used. The exception is in the Ceremonial of Bishops (Caeremoniale Episcoporum), in describing the Stational Mass of the Diocesan Bishop, n. 149: “… The bishop receives the censer from the deacon and, in the same way as at the beginning of Mass and accompanied by a deacon, incenses the gifts, as well as the altar and the cross. After this, all rise, and a deacon, standing at the side of the altar, incenses the bishop, who stands without the miter, then the concelebrants, then the people.” There are no directions for the people to sit. So a unique feature of the Stational Mass is that all stand when the thurible is passed from the bishop to the deacon. (Reference: Ceremonial of Bishops, Liturgical Press, 1989, ISBN 0-8146-1818-9, page 56.)
From the 2002 General Instruction of the Roman Missal (GIRM):
“112. … At a Mass celebrated by the Bishop or at which he presides without celebrating the Eucharist, the norms found in the Caeremoniale Episcoporum should be observed.”
