As has been noted, it will vary between orders, and for Benedictines at least, between individual monasteries (it’s been joked that it’s really called the Benedictine Disorder…). The best place for the information is in the abbey’s “customary”, a book that summarizes all the customs specific to a particular house. The abbey’s library has some old customaries from other houses, and that would probably give some great insight. I’ll describe briefly how it works at our abbey. Even though it uses a monastic post-Conciliar liturgy, their customs are rooted in tradition and probably haven’t changed much.
Introductory verse (or Invitatory): standing.
Invitatory psalm (94): standing, except kneel at the words “Come, then, let us bow down and worship, *
bending the knee before the Lord, our maker.”; bow at the doxology.
Hymn (Vigils and minor hours): Standing, except for bow at the doxology (a handful of Latin hymns do not have a doxology so remain standing).
Psalmody (including OT Canticle at Lauds): stand for the first antiphon and incipit, then sit through the psalmody; rise at the second hemistich of the last verse, and bow at the doxology, then sit through the next psalm (the cantor who intones the antiphon stands through it)
Reading: lector reads from the ambo, the rest sit and listen
Responsory: stand, bow at the Gloria Patri
Hymn: stand, bow at doxology except remain standing at the few hymns that have no doxology
Ornate verse: stand
Gospel canticle antiphon: Stand at the incipit, then lean on misericords through the rest of the antiphon.
Gospel Canticle: stand and make the sign of the cross at the opening verse; remain standing and bow at the doxology.
Kyrie, Pater and Collect: stand
Blessing: bow deeply (Benedictines do not cross themselves at the final blessing)
Benedicamus Domino, invocation for deceased brothers, invocation for absent brothers: stand.
Compline is a bit different:
Stand for opening verse
Bow at Confiteor and words of absolution
Lean against misericords through the psalmody, bowing at the doxology
Stand for the hymn and bow at its doxology
Lean against misericords for the reading
Stand for the verse (in the Benedictine tradition there is no responsory nor Gospel Canticle, but some houses since the council include them)
Or if there’s a responsory and Gospel canticle,
Stand for the responsory, bow at the gloria patri,
Stand for the Gospel Canticle, crossing yourself at the opening verse
Stand for the Kyrie, (pater in secret), collect, final blessing and invocation for absent brothers
Stand for the Marian Antiphon
Bow and cross yourselves at the superior’s sprinkling with holy water.
That sums it up. In the modern office, which our abbey uses, there are intercessions; one stands through those except in Lent when one kneels throughout until the final blessing.
Again, other houses and other orders will have some variations.