Jesus, Peter, James, and John went up into a high mountain. Jesus was “transfigured” and his face did shine as the sun, and his raiment was white as the light.” Moses and Elias appeared. Peter wanted to make 3 tabernacles one for each Jesus, Moses, & Elias. A cloud came and said “This is my beloved Son, in whom I am well pleased; hear ye him,” then Jesus appear in glory and prophesied of his death and resurrection. The apostles were eyewitnesses and fell to the earth because they were frightened. Jesus came to comfort them and tell them not to be afraid. THe apostles got up and looked around and saw only Jesus. The most important part of the Appearance of Moses and Elijah was to To pass down the keys of the priesthood to James, Peter, John and be able to act as the first presidency.
Bible Dictionary; Transfiguration, Mount Of.
“This very important event in the New Testament occurred about a week after the promise made to Peter that he would receive the keys of the kingdom of heaven (Matt. 16:13–19; 17:1–9). On the mount, the Savior, Moses, and Elias (Elijah) gave the promised keys of the priesthood to Peter, James, and John (HC 3:387), which enabled these brethren to carry forth the work of the kingdom on the earth after the departure of Jesus. These keys were later given to all of the Twelve. The Transfiguration occurred in about October, some six months before the death of Jesus. The brethren saw the Lord in a glorified and transfigured state. They also saw a vision of the earth as it will appear in its future glorified condition (D&C 63:20–21; HC 1:283); saw and conversed with Moses and Elijah, two translated beings; and heard the voice of the Father bearing witness that Jesus is His beloved Son, in whom the Father is pleased, and commanding the brethren to hear (obey) Him. See also Mark 9:2–10; Luke 9:28–36; 2 Pet. 1:16–18. The event is important in many ways: Necessary priesthood authority was conferred upon Peter, James, and John; the significance of the Savior’s work was emphasized; and the unity of various dispensations and the close relationship of Jesus and His prophets was demonstrated. Few events in the Bible equal it in importance. A similar event occurred on April 3, 1836, in the temple at Kirtland, Ohio, where the same heavenly messengers conferred priesthood keys upon the Prophet Joseph Smith and Oliver Cowdery (D&C 110).”
2. In what ways would this experience have prepared the three Apostles for the responsibilities they would soon have as leaders of the Church?
I think they would no longer have faith that Jesus was the Christ they would know for sure because they say two dead profits and heard the voice of heavenly father. This would strengthen they for their tasks ahead so they could stand by Christ and help him as much as they could with weak mortal bodies.