(from various sources by Nikita Simmons)
Q: When reading the Psalter, is there a difference in how the Psalter for the departed, as opposed to reading the Psalter as a prayer rule?
A: Yes. When reading the Psalter as a prayer rule, the Troparia and prayers that are included in the Psalter (usually following each Kathisma) are read. (There are special rubrics for concluding the Psalter at any place, and continuing the reading at a later time.)
However, when reading the Psalter for the reposed, the usual prayers are NOT read, rather one specific prayer "Remember, O Lord our God, Thy servant..." (see below; found on p. 107, St Tikhon's Great Book of Needs, vol. 3; also at the back of the HTM Psalter) is read after each full Kathisma (or after each stasis of each Kathisma, according to some sources). All other troparia and prayers are omitted. The Canon for One Who is Departed is then read after finishing the Psalter, and the (next) reader begins the Psalter all over again.
After each Kathisma we say the Trisagion-Our Father, Lord Have Mercy (40 times), then this prayer:
Prayer for every departed person
Remember, O Lord our God, Thy servant, our brother/sister, N., who has reposed in the Faith and hope of life eternal, and in that Thou art good and the lover of mankind, Who remittest sins and blottest out iniquities, do Thou loose, remit and pardon all his/her sins, voluntary and involuntary. Deliver him/her from eternal tormet and the fire of Gehenna, and grant unto him/her the communion and delight of Thine eternal good things prepared for them that love Thee. For though he/she hath sinned, yet hath he/she not forsaken Thee, and he/she undoubtedly believed in the + Father and the Son and the Holy Spirit; and even until his/her last breath did he/she confess Thee in Orthodox fashion: God glorified in Trinity, Unity in Trinity and Trinity in Unity. Wherefore, be Thou merciful unto him/her and reckon his/her faith in Thee, rather then his/her deeds, and in that Thou art compassionate, grant him/her rest with Thy saints; for there is no man that liveth and doth not sin. But Thou alone art wholly without sin, and Thy truth is forever; and Thou alone art the God of mercies, and compassion, and love for mankind, and unto Thee do we ascribe glory, to the Father, and to the Son and to the Holy Spirit, now and ever, and unto ages of ages. Amen.