The best way is to have Masses said for them. If you cannot do that, you ought to hear Mass for them (you should offer every Mass you attend for a personal intention, which, if you want to help the Holy Souls, should be for them). Now, as far as private prayer, I can suggest prayers from the Masses for the Dead:
uvoc.org/Holy_Souls/Holy_Souls.html
Those are the Masses for the Dead (there are three), according to the Traditional Latin Mass. You can really use all of the propers for prayers, but I would think the Epistle/Lesson, Gospel, and maybe the Preface would be least becomng. But, you can use what you will.
Here are some other prayers for those in Purgatory and for the dying:
PRAYER OF ST. GERTRUDE THE GREAT
O Eternal Father, I offer Thee the Most Precious Blood of Thy Divine Son, Jesus, in union with the Masses said throughout the world today, for all the holy souls in Purgatory and for sinners everywhere – for sinners in the universal Church, for those in my own home and in my own family. Amen.
(It is private revelation that 1000 souls are released from Purgatory every time this prayer is said.)
PRAYER FOR THE DYING
O Most Merciful Jesus, lover of souls, I pray Thee, by the agony of Thy most Sacred Heart, and by the sorrows of Thine Immaculate Mother, to wash in Thy Most Precious Blood the sinners of the whole world who are now in their agony and who will die today.
Heart of Jesus, once in agony, have mercy on the dying!
Amen
This website has some good prayers, as well:
home.flash.net/~oramus/nov_souls.html
The “De Profundis” mentioned on that site are the first words of Ps. 129, which in its entirety is: Out of the depths I have cried to thee, O Lord: Lord, hear my voice. Let thy ears be attentive to the voice of my supplication. If thou, O Lord, wilt mark iniquities: Lord, who shall stand it. For with thee there is merciful forgiveness: and by reason of thy law, I have waited for thee, O Lord. My soul hath relied on his word: My soul hath hoped in the Lord. From the morning watch even until night, let Israel hope in the Lord. Because with the Lord there is mercy: and with him plentiful redemption. And he shall redeem Israel from all his iniquities.
It may only be referring to the first part, though, which is from the Mass for the dead (the Introit): De profundis clamavi ad te, Domine: Domine exaudi vocem meam. De profundis clamavi ad te (Out of the depths I have cried to thee, O Lord: Lord, hear my voice. Out of the depths I have cried to thee.)