How did Jesus' Transfiguration prepare the apostles for His subsequent crucifixion?
Much of the meaning of a particular event is revealed in the holy services, especially Vespers and Matins. This is why it is absolutely necessary for a Christian to zealously attend the Vigil service. The services, and the commentaries of the holy fathers, which have entered into the mind of the church, explain that the apostles were prepared for the crucifixion by witnessing the Transfiguration, and the "splendor of the resurrection" that it prefigured. They would soon be subjected to terrible temptations and fears, and our Savior wanted to put the knowledge of His divinity indelibly in their minds, to help them in the terrible days of his trial and death.
Kontakion of the Feast, Tone 7
On the mountain wast Thou transfigured, / and Thy disciples beheld Thy glory as far as they could bear it, O Christ God; / that when they would see Thee crucified, / they would comprehend that Thy suffering was voluntary, / and proclaim to the world that Thou art of a truth // the Effulgence of the Father.
Before Thy crucifixion, O Lord, / the mountain emulated the heavens, / and the cloud spread itself out like a tabernacle / when Thou wast transfigured and borne witness to by the Father. / There were Peter, James and John, / for they were to be with Thee also at the time of Thy betrayal, / that, beholding Thy wonders, / they might not be afraid of Thy sufferings, / which do Thou vouchsafe that we may venerate in peace, // for the sake of Thy great mercy. ( First Sticheron of the Feast for Lord I have cried, Tone 4)
Taking the disciples up upon the lofty mountain / before Thy crucifixion, O Lord, / Thou wast transfigured before them, / illumining them with effulgence of power, / desiring both in Thy love for mankind and in Thine authority / to show them the splendor of the resurrection, / which do thou vouchsafe unto us in peace, // in that Thou art merciful and lovest man-kind. (Third Sticheron of the Feast for Lord I have cried, Tone 4)
"But Peter and they that were with him were heavy with sleep: " (vs. 32)
Why were they heavy with sleep?
"Then to show that he was holden with great fear, both he and the rest, he saith, "They were heavy with sleep, and when they were awake they saw His glory;"25 meaning by deep sleep here, the deep stupor engendered in them by that vision. For as eyes are darkened by an excessive splendor, so at that time also did they feel. For it was not, I suppose, night, but day; and the exceeding greatness of the light weighed down the infirmity of their eyes." (St John Chrysostom)
"And when the voice was past, Jesus was found alone. And they kept it close, and told no man in those days any of those things which they had seen. " (Luke 9:36)
Why did the Apostles tell nobody about this startling event?
Jesus ordered his three disciples to say nothing about His transfiguration:
" And as they came down from the mountain, Jesus charged them, saying, Tell the vision to no man, until the Son of man be risen again from the dead." (Matthew 17:9)
The Lord told them to be quiet so that people would not be scandalized when they saw him on the cross. He saved this knowledge only for His three favorites, because He knew it would help them.