II Maccabees 12:43-46: "And making a gathering, he [Judas] sent twelve thousand drachms of silver to Jerusalem for sacrifice to be offered for the sins of the dead, thinking well and religiously concerning the resurrection, (For if he had not hoped that they that were slain should rise again, it would have seemed superfluous and vain to pray for the dead,) And because he considered that they who had fallen asleep with godliness, had great grace laid up for them. It is therefore a holy and wholesome thought to pray for the dead, that they may be loosed from sins."

Those who've died in a state of grace are not truly "dead"; they are our beloved in Heaven or in Purgatory (on their way to Heaven) and will forever be, world without end, part of the Communion of Saints -- the Church Triumphant (the Saints in Heaven, whether or not they are beatified or canonized), the Church Suffering (the saints in Purgatory), and the Church Militant (the saints on earth).

Because, aside from those the Church has beatified or canonized, we can't know who is already in Heaven, who is in Purgatory for a time, or who is damned, we pray for the dead for the rest of our lives -- assuming they are in Purgatory, while hoping they are in Heaven and not damned. This has been the practice of Christians since the beginning of the Church, as attested to by inscriptions found in the catacombs, such as this one found in the Catacombs of  Domitilla:

We also ask those who've died to pray for us. While those whom the Church has deemed to be of the Church Triumphant (the canonized Saints) are in Heaven for certain and are, therefore, in no need of our prayers for them, we've always asked for them to pray for us.

As to the Church Suffering in Purgatory (the "poor souls"), Aquinas teaches that they are not able to know, by themselves, our prayers; however, it is piously believed, and taught by St. Alphonsus Liguori, that God makes our prayers known to them -- not directly, as they are deprived of the Beatific Vision until they enter Heaven, but by infusing this knowledge into their souls. St. Bellarmine teaches that because the Church Suffering is so close to God -- much closer than we are and having the great consolation of knowing they are saved -- their prayers for us are very effective. So, as you pray for your dead loved ones, ask them to pray for you, too! This practice, too, is attested to in the ancient catacombs, these coming again from the Catacomb of Domitilla:

As to the damned, there is no hope; no prayer can help them and we can't pray formally for those in Hell. The problem, of course, is that we can't know who is damned, and so we pray generally for "all the faithful departed." For those who've died outside of visible Communion with Christ's Church or for those Catholics who've died seemingly without repentance and in scandal, public prayer cannot be offered, but we can most certainly still pray privately with the hope that they've died in a state of grace. Those who are denied a Catholic funeral can't be prayed for liturgically, publicly, but they can most definitely be prayed for -- and should be prayed for -- privately. Priests can even offer Masses for such people privately, without naming them.

Private Prayer
for the Dead

In addition to having a Mass said on the anniversary of a loved one's death as mentioned above, there exists an old Christian custom of fasting, burning a candle for 24 hours, and praying for them on this day and on future anniversaries of the loved one's death (this custom was adopted by Jews in the Middle Ages; they call it "Jahrzeit" -- also spelled "Yahrzeit" --  as did the medieval German Christians.) Any orthodox traditional or improvised prayer can be prayed at this time, but the Rosary is always appropriate and can be prayed now (or any time) for the dead, offered in the same way it is at Catholic funerals -- i.e., with the Fatima Prayer replaced by the Eternal Rest Prayer. The Eternal Rest prayer is also prayed by itself, offered any time for the dead, when visiting grave sites, and when passing cemeteries. It is a prayer every Catholic should know by heart:

We also pray for our dead every time we eat if we pray the After Meal Blessing, another prayer every Catholic should know by heart:
 

The Penitential Psalms -- i.e., Psalms 6, 31, 37, 50, 101, 129, 142 -- are also prayed for the dead, especially the 129th Psalm, known as De Profundis (Out of the Depths):
 

 

The Prayer of St. Gertrude the Great

Another prayer Catholics should be familiar with is that of St. Gertrude the Great (A.D. 1256-1301/2), who was told by Our Lord in a private revelation, that when the following prayer is prayed earnestly, 1,000 souls will be released from Purgatory. This is not an official Catholic teaching, mind you, and the revelation may have only applied to St. Gertrude's prayers; but the prayer is a good one nonetheless. Because of the desire to unite the prayer with the merits of the Mass, it is most powerful:

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, for sinners everywhere, for sinners in the Universal Church, those in my own home and within my own family. Amen.

 

Heroic Act of Charity
 
An "Heroic Act of Charity" is the offering of the satisfactory value (not the merits) of all of our sufferings and works of our rest of our lives and of any time we may spend in Purgatory for the relief of the souls in Purgatory. We do this by first deciding to do so, and then praying (using our own words or the more formal prayer below) to offer these things to God through Mary's hands.

Doing this is not a matter of taking a vow; it doesn't bind under pain of sin, and it is revokable (unless one vows never to revoke the Act). But it is a tremendous sacrifice, hence the name. It is truly heroic, a giving up of one's own earned relief from the temporal effects of sin -- even relief of the sufferings of Purgatory -- for the good of others.

In addition to asking God to use their satisfactory works for the souls in Purgatory, those who make this Act also receive a plenary indulgence (under the usual conditions) for the souls in Purgatory each time they receive Communion, and each time they hear Mass on Mondays for the sake of the departed. Words to a formal Act of Heroic Charity are as follows:

O Holy and Adorable Trinity, desiring to aid in the relief and release of the Holy Souls in Purgatory, through my devotion to the Blessed Virgin Mary, I cede and renounce, on behalf of these souls, all the satisfactory part of my works, and all the suffrages which may be given to me after my death. In their entirety, I offer them to Mary, the Most Holy Mother of God, that she may use them, according to her good pleasure, for those souls of the faithful departed whom she desires to alleviate their suffering. O my God, deign to accept and bless my offering which I make to Thee through the most august Queen of Heaven and Earth. Amen.