Mass

The first instalments of the Latin Noted Missal are now available.
Latin Noted MIssal
Latin Gloria Patri at the Officium (Introit)
Latin Sequentiarium
Indices

The English Noted Missal is in preparation.
English Noted Missal
English Gloria Patri at the Officium (Introit).  (Palmer and Burgess, The Plainchant Gradual 1946/R 1965:302-304 includes the Sarum version of the Tones for the Gloria Patri in English, even though the proper chants of the mass are the Roman forms.)
While the above is in preparation, a Beta edition of the  Sarum English Performing Gradual is available as of July 2012.

Performance notes on the proper chants.

Officium
The antiphon is intoned by one or more leaders, and taken up by the full choir.  On Sundays and Feasts of Saint with Rulers of the Choir, and within ruled Octaves, and on Masses of St. Mary and the Feast of the Place, the antiphon is repeated after the psalm-verse–before the ‘Gloria Patri’–and again after the ‘Gloria Patri’:
-Antiphon
-Psalm-Verse
-Antiphon
-Gloria Patri
-Antiphon
When the Choir is not ruled the first repetition of the antiphon is omitted.
-Antiphon
-Psalm-Verse
-Gloria Patri
-Antiphon
During Passiontide the ‘Gloria Patri’ is omitted.
-Antiphon
-Psalm-Verse
-Antiphon
I have yet to see Sarum rubrics indicating who is to sing the psalm-verse and the ‘Gloria Patri’.  The typical Roman practice today is for a leader to sing the psalm-verse up to the mid-point (colon or *), at which point the full choir continues; and likewise for a leader to sing the ‘Gloria Patri’ up to the end of ‘Spiritui Sancto’, at which point the full choir continues.

Gradual
Normally one or more leaders intone the responsory after which the full choir commences the responsory again from the beginning and continues until the verse.   The leaders sing the verse; the full choir joins in for the final word(s) of the verse.  The leaders again intone the responsory, after which the full choir again commences the responsory from the beginning and concludes it.

On certain occasions the repetition of the responsory is omitted.  They are: double feasts (except the second mass of Christmas), the fifth and sixth days of Easter, the ‘four seasons’ (ember days), and generally when a Tract follows.

Exceptions to these principles are noted in the text.

(If circumstances require a solo performance it would be appropriate to omit the repetitions of the incipit.)

Alleluya
Normally one or more leaders intone the Alleluya, after which the full choir commences the Alleluya again from the beginning and continues to the end of the neuma (jubilus). The leader(s) sing the verse; the full choir joins in for the final word(s) of the verse.  If a sequence shall follow, the leader(s) again intone the Alleluya. If there is no sequence, the leader(s) again intone the Alleluya, after which the full choir again commences the Alleluya from the beginning and concludes it with the neuma (jubilus).

(If circumstances require a solo performance  it would be appropriate to omit the repetitions of the incipit.)

Sequence
There appear to be no specific Sarum rubrics pertaining to the performance of the sequence. It would seem appropriate for the leader(s) to begin (up to the editorial ‘*’), and for the Choir side to continue to the end of the first line (double bar). From there to the end a continuation alternating by sides of the choir would seem most appropriate.  It may be appropriate for the final line of the sequence to be sung by the full choir.

Offertory
It would appear that the offertory is intoned by one or more leaders and is continued and concluded by the full choir.

Offertory Verse
Offertory verses are sung during the week.  I have yet to see Sarum rubrics pertaining to the performance of the offertory verse.  It presumably would follow the pattern of the Gradual, that is, sung by one or more leaders.  However, it is not clear whether the verse is concluded by the full choir or not, and it is not clear whether the responsory is repeated after the verse.  Given that the Offertory Verse is often tonally open at the end, and that no other musical item follows it directly (as the Alleluya may follow directly after a Gradual Verse, or a Sequence may follow directly after a repetition of Alleluya repetition–omitting the jubilus), it would make the most sense to repeat the whole responsory.  (The Roman practice seems to be to repeat the latter part of the responsory as a repetenda.)

Communion
It would appear that the communion is intoned by one or more leaders and is continued and concluded by the full choir.  The Sarum Rite does not include Communion Verses.