The following is an excerpt from Catholic.com (full text), and published with the Nihil Obstat approval. It is only extracted text, with no other modifications.
Some may grant that the previous objections to asking the saints for their intercession do not work and may even grant that the practice is permissible in theory, yet they may question it on other grounds, asking why one would want to ask the saints to pray for one. "Why not pray directly to Jesus?" they ask.
The answer is: "Of course one should pray directly to Jesus!" But that does not mean it is not also a good thing to ask others to pray for one as well. Ultimately, the "go-directly-to-Jesus" objection boomerangs back on the one who makes it: Why should we ask any Christian, in heaven or on earth, to pray for us when we can ask Jesus directly? If the mere fact that we can go straight to Jesus proved that we should ask no Christian in heaven to pray for us then it would also prove that we should ask no Christian on earth to pray for us.
Praying for each other is simply part of what Christians do. As we saw, in 1 Timothy 2:1–4, Paul strongly encouraged Christians to intercede for many different things, and that passage is by no means unique in his writings. Elsewhere Paul directly asks others to pray for him (Rom. 15:30–32, Eph. 6:18–20, Col. 4:3, 1 Thess. 5:25, 2 Thess. 3:1), and he assured them that he was praying for them as well (2 Thess. 1:11). Most fundamentally, Jesus himself required us to pray for others, and not only for those who asked us to do so (Matt. 5:44).
Since the practice of asking others to pray for us is so highly recommended in Scripture, it cannot be regarded as superfluous on the grounds that one can go directly to Jesus. The New Testament would not recommend it if there were not benefits coming from it. One such benefit is that the faith and devotion of the saints can support our own weaknesses and supply what is lacking in our own faith and devotion. Jesus regularly supplied for one person based on another person’s faith (e.g., Matt. 8:13, 15:28, 17:15–18, Mark 9:17–29, Luke 8:49–55). And it goes without saying that those in heaven, being free of the body and the distractions of this life, have even greater confidence and devotion to God than anyone on earth.
Also, God answers in particular the prayers of the righteous. James declares: "The prayer of a righteous man has great power in its effects. Elijah was a man of like nature with ourselves and he prayed fervently that it might not rain, and for three years and six months it did not rain on the earth. Then he prayed again and the heaven gave rain, and the earth brought forth its fruit" (Jas. 5:16–18). Yet those Christians in heaven are more righteous, since they have been made perfect to stand in God’s presence (Heb. 12:22-23), than anyone on earth, meaning their prayers would be even more efficacious.
Having others praying for us thus is a good thing, not something to be despised or set aside. Of course, we should pray directly to Christ with every pressing need we have (cf. John 14:13–14). That’s something the Catholic Church strongly encourages. In fact, the prayers of the Mass, the central act of Catholic worship, are directed to God and Jesus, not the saints. But this does not mean that we should not also ask our fellow Christians, including those in heaven, to pray with us.
In addition to our prayers directly to God and Jesus (which are absolutely essential to the Christian life), there are abundant reasons to ask our fellow Christians in heaven to pray for us. The Bible indicates that they are aware of our prayers, that they intercede for us, and that their prayers are effective (else they would not be offered). It is only narrow-mindedness that suggests we should refrain from asking our fellow Christians in heaven to do what we already know them to be anxious and capable of doing.
In Heaven and On Earth
The Bible directs us to invoke those in heaven and ask them to pray with us. Thus in Psalms 103, we pray, "Bless the Lord, O you his angels, you mighty ones who do his word, hearkening to the voice of his word! Bless the Lord, all his hosts, his ministers that do his will!" (Ps. 103:20-21). And in Psalms 148 we pray, "Praise the Lord! Praise the Lord from the heavens, praise him in the heights! Praise him, all his angels, praise him, all his host!" (Ps. 148:1-2).
Not only do those in heaven pray with us, they also pray for us. In the book of Revelation, we read: "[An] angel came and stood at the altar [in heaven] with a golden censer; and he was given much incense to mingle with the prayers of all the saints upon the golden altar before the throne; and the smoke of the incense rose with the prayers of the saints from the hand of the angel before God" (Rev. 8:3-4).
And those in heaven who offer to God our prayers aren’t just angels, but humans as well. John sees that "the twenty-four elders [the leaders of the people of God in heaven] fell down before the Lamb, each holding a harp, and with golden bowls full of incense, which are the prayers of the saints" (Rev. 5:8). The simple fact is, as this passage shows: The saints in heaven offer to God the prayers of the saints on earth.
NIHIL OBSTAT: I have concluded that the materials
presented in this work are free of doctrinal or moral errors.
Bernadeane Carr, STL, Censor Librorum, August 10, 2004
IMPRIMATUR: In accord with 1983 CIC 827
permission to publish this work is hereby granted.
+Robert H. Brom, Bishop of San Diego, August 10, 2004
And here is another link that is quite good:
Also, it is worthwhile to point out that the early Christians had this practice of begging for the intercession of the saints. They even venerated the relics of the Christian martyrs not only by risking their lives to bury their bodies, but also by celebrating Mass over their tombs. This tradition is still with the Church, as every consecrated altar where Mass is publicly celebrated is to have relics of saints underneath. We recognize the holy souls of saints in humility, and give them proper respect for honor of God. Furthermore, we ask for their intercessions, because they are already united to Him in Heaven, where their prayers are more efficacious than ours alone. While we are the Church Militant, they are the Church Triumphant.