Divination, which is what the Bible prohibits, is "a foreseeing or foretelling of future events; the pretended art discovering secret or future by preternatural means," thus placing your trust outside of God (Webster's Revised Unabridged Dictionary, © 1996, 1998 MICRA, Inc.) This is not what we do when we ask saints for their prayers.
Revelation 8:3-4 records this scene from John's vision of Heaven, "And another angel came and stood at the altar 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."
Through that vision, we have a clear picture of worship in Heaven, complete with an angel offering up the prayers of the Saints. The angels and Saints in Heaven stand before Christ in worship, perfectly living out the commands of Christ, one of which is that we pray for one another. It is their love for us as brothers, and more importantly Christ within us, that drives them to pray for us. The same Jesus that dwells in our hearts dwells in theirs as they partake fully in the "divine nature," and that is the tie that binds us together in the Communion of Saints.
Here is a good example of divination from the Old Testament, and an explination of why it is forbidden. Some bring it up as an argument against prayer to Saints, but I do not believe it applies. In this example, Saul does not go to Samuel in holy prayer as a brother in the Lord, with confidence in God's answering his request, instead he went to a medium to divine the future, showing his distrust and turning from God. 1 Samuel says, "...when Saul inquired of the LORD, the LORD did not answer him, either by dreams, or by Urim, or by prophets. Then Saul said to his servants, 'Seek out for me a woman who is a medium, that I may go to her and inquire of her.' "
As was said before, divination is "The act of divining; a foreseeing or foretelling of future events; the pretended art discovering secret or future by preternatural means." Our prayers to Saints are not turns away from God, as was Saul's journey into divination, they are, instead, acts of faith in God who we believe overcame death and has given us the greatest gift, eternal life and participation in the Body of Christ.
I hope it can now be clearly seen that Saul's divination and the Catholic/Coptic/Orthodox practice of asking Saints for prayer are completely different in form and intent.