From Orthodox Prayer
In our prayer rule we can also ask the saints to intercede for us and to help us in our worldly struggles. Saints are those holy individuals who have died as martyrs, who have made a fearless confession of faith often with the threat of death, who have demonstrated self-sacrificing service, who have a special gift of healing and perform miracles after their death when remembered in prayer.
These holy people the Lord calls his friends. You are my friends if you do whatever I command you. No longer do I call you servants, for a servant does not know what his master is doing; but I have called you friends, for all things that I heard from my Father I have made known to you. (John 15:14-15)
They are those he has received in his Heavenly mansions in fulfillment of his words: Where I am, there you may be also. (John 14:3) Instead of praying for forgiveness of their sins, we praise them for their struggles in Christ. We make petitions to them asking them to pray for us and the remission of our sins and spiritual growth, seeking their help in our spiritual needs.
The saints are near the throne of God.
Then I looked, and I heard the voice of many angels around the throne, the living creatures, and the elders; and the number of them was ten thousand times ten thousand, and thousands of thousands, who praised the Lord. (Revelation 5:11)
Our communion in prayer with the saints is the realization of the bond between Christians on Earth and the Heavenly church. (Hebrews 12:22-23)
Sacred scripture presents numerous examples that the righteous, while still living can see and hear and know much that is inaccessible to the ordinary understanding. The saints while they were still on Earth were able to penetrate in spirit into the world above.
From the parable of the rich man and Lazarus (Luke 16:10-31) we know that Abraham being in Heaven could hear the cry of the rich man who was suffering in hell, despite the great unbridgeable gulf that separates them.
The church has always taught the invocation of the saints, convinced they intercede for us before God in Heaven. Having a prayer relationship with a saint is another way that we can gain help in our spiritual path to salvation in the church.
Facing up to Mary (pdf): a nice summary for those who have concerns about the whole subject of Mary (Mother of God).
Prayer and the Departed Saints By David C. Ford, Ph.D
On the Intercession and Invocation of the Saints by Reader Christopher Orr; A Protestant’s inquiry
Most Holy Theotokos, Save Us by Fr. Aris Metrakos
What we Believe about the Saints By Anthony M. Coniaris
The Place of Lives of Saints in the Spiritual Life
By Hieromonk Damascene
The saints are called stars in the spiritual firmament. May we, by remembering the saints of God, also begin to shine in that firmament. And by making the saints our friends and preceptors now, may we have them as our Heavenly companions in the never-ending Kingdom of Light.
Book: The Orthodox Veneration of Mary The Birthgiver of God, by Saint John Maximovitch, Saint Herman of Alaska Brotherhood, 1996.
A right understanding of Mary the Birthgiver of God is essential for a right understanding of Jesus Christ, the Son of God. When her image is distorted, the image of her Son becomes distorted, also. This concise little book is a classic exposition of how the historic Christian church has venerated the Mother of God throughout the ages, and on the chief errors which have attacked this veneration. It clearly tells why the virgin Mary should be honored by all generations, and why at the same time she cannot be considered a co-Redemptress along with Jesus Christ, the only savior of the world.
And another angel came, and stood before the altar, having a golden censer; and there was given to him much incense, that he should offer of the prayers of all saints upon the golden altar, which is before the throne of God. And the smoke of the incense of the prayers of the saints ascended up before God from the hand of the angel. (Apocalypse: 8: 3-4)