There are many and diverse ways to pray for the relief of the souls in purgatory. Of course, they cannot pray for themselves, but rather they suffer the full penalty in order that they may pay "to the last farthing" their debt owed to God due to their sins. In confession, our guilt is forgiven (assuming a good confession) but our entire debt remains. In order to pay this debt we must do penance in this life. What we do not pay in this life, we will pay in the next in purgatory. This is a truth of our Catholic faith, a dogma which all Catholics are bound to believe.
In assisting the suffering souls in Purgatory, we are in a manner paying their debts for them. We can pray for them, offer sacrifices for them, receive Communion, even simply offer our daily work and tasks on their behalf. In helping them, we do in a sense visit God's prisoners - if we practice a regular devotion in paying down their debts, we may hear our Lord on the last day say to us..."Come ye into the house of my Father, for I was in prison, and you visited Me." It is the greatest hope of my life to hear those words from Jesus' lips.
Also, don't forget!....In helping them pay their debts - you pay yours! Many theologians have said this is far more efficacious then great fasting and austerities because you add charity to prayer!
Here are some other ways we can help them who suffer night and day, without the slightest rest or relief:
1. What is this sin/weakness/fault from which you suffer the most? Impure thoughts? Pray for the souls who suffer due to sins of impurity. Overly attached to the pleasures of the table? Overweight? Pray for those who suffer due to sins of gluttony! Are you a secret thief? Pray for thieves! And so on...you get the idea. God will not be outdone in charity. If you help others who suffer from sins like yours, He will speedily come to your aid. Also - the souls whom you help, you are assured of their prayers as well. They will fly to heaven because of your charity, bow down before the throne of God and never cease to pray for you until you are right there beside them.
2. Do you pray the rosary? At the end of each decade, I suggest this simply prayer: "Eternal Father, I offer all the blood which your Divine Son shed in the Garden of His Agony, together with all the masses said throughout the world today, in payment of the debts of the souls in Purgatory, especially those (suffer from their sins of gluttony/my family/my dear mother/etc). Eternal rest grant onto them/him/her, O Lord, may eternal light shine upon them. May they rest in peace.
As you pray the sorrowful mysteries, offer the Blood of Jesus to the Father, the joyful mysteries offer the Father hands of Mary who held her Son, etc. I especially like offering the footsteps of Jesus as He walked to Bethany before the Ascension. Be creative and let this add to your contemplation of God's wondrous deeds.
3. When you approach the holy water font, splash a few drops on the floor for those suffering fire.
4. When you are insulted, mistreated by others, resolve to suffer with patience and offer this in payment and atonement for them. You gain merit for your patience, but how much for in giving away the penitential portion of your suffering to others?
5. This is one I do alot - if you have children, at the end of the day, when you're tired and just want some peace but they want your attention or need your help with some task, instead of sighing and refusing or doing their bidding with reluctance, resolve to be joyful exteriorly (though you may be griping and shrinking interiorly) and offer this for the suffering souls! They will repay you a hundredfold!
6. Do you do housework? Try this one: as you clean the floor, scrub your toilet/tub/sink/etc - act as if you are cleaning the dwellings of those in purgatory. Offer every movement of your hands and feet, every effort and drop of sweat for them. You get your house clean, and you do great charity at the same time.
7. Do you drive long distances? Ask the Lord with every mile marker/town/state/etc to release a soul from purgatory. Pray the rosary while you drive/fly/etc and ask Jesus to release a soul for every Hail Mary - the possibilities are endless.
There are many, many other small and various ways in which we can help them. We simply need to be mindful and the Holy Spirit will guide us. With time and practice you may find that every single thing you do, every thought, every step - you can be helping those who need you so much! If you have other practices for assisting those in purgatory, please leave them in the combox.