First up to "the plate" is Matthew's contribution. The first time prayer is mentioned or associated with Jesus is when He teaches on the subject, sitting on a mountainside, by giving a pattern (commonly referred to as The Lord's Prayer) which to follow and supplying instructions to keep prayer sacred (Matthew 8:5-13).
The next time prayer is brought up is when Jesus actually prays. Jesus' first direct prayer to Father God is a prayer that could entitle Father God - "Revealer". This prayer was prayed at a time when people were not repenting in the cities where He performed His miracles (11:20). He was in the towns of Galilee when He prayed this prayer.
You have heard of "Saying Grace", as in saying a prayer or blessing over the food before you eat. Well, check out Matthew 14:19 and you will find a prayer of thanksgiving, during the evening hours, over the coming miraculous meal (Feeding of Five Thousand).
Then after the Feeding of Five Thousand and before Jesus Walks on Water, He "went up on a mountainside by himself and prayed." You will find that mountainsides and lakes are favorite locales by my Lord. The time-frame was afternoon-to-evening because of Matthew 14:23. We do not know for sure what He prayed, it does not say. Matthew 14:23-24.
On another mountainside (I told you), by the Sea of Galilee, Jesus once again gave thanks for another miracle-meal for four thousand - Matthew 15:36.
In Matthew 19:13-15, little children were brought to Jesus for Him to touch and pray, but He only touched them, according to verse 15. This might have been an impartation of what the children needed. To mention hands and prayer one time and only hands the next time is not accidental in my humble opinion. Interesting.
After finishing their meal, Jesus and His Disciples reclined at the table and Jesus gave thanks and blessed the Passover Bread and Wine (Matthew 26:26-27). So there has been a thanking and/or blessing of the food now three times where concerning prayer and Jesus. I think it is important. What do you think?
The Gethsemane Prayers (Matthew 26:36:42) - First Jesus prayed WITH Peter and two sons of Zebedee until "He was overwhelmed with sorrow to the point of death!" Second, He prayed, "let this cup pass from me" or please, Father, let this way not be the way, yet not my will or plan, but yours be accomplished. He prays this prayer two more times!
Finally, on The Cross, Jesus cries out to Father God, "'My God, My God, why have you forsaken me?'" This is a type of prayer - crying out to God. I am glad my Savior cried out so I could have the privilege of doing the same. Matthew 27:46
Mark's donation is very brief. Mark 1:35 - "Very early in the morning, while it was still dark, Jesus got up, left the house and went off to a solitary place, where he prayed." When? "very early in the morning". Where? "a solitary place" outside the house - "Jesus got up, left the house". What did He pray? We don't know for sure.
Luke followed up right on Mark's heels with Jesus' criteria for prayer. Observe Luke 5:16 - "But Jesus often withdrew to lonely places and prayed." This is not surprising with the masses of people that flocked to Him for all the healings that they needed in their lives.
I have another mountainside story for you (Luke 6:12). This time it is an all-nighter and we might be able to take an educated guess at what Jesus would have prayed by observing verse 13. The original verse reads - "One of those days Jesus went out to a mountainside to pray, and spent the night praying to God." Well, we know where and when. The next verse says, "When morning came, he called his disciples to him and chose twelve of them, whom he also designated apostles:..." Before this night, it seems Jesus had many followers. During the night, His prayer might have been for direction in selecting the Apostles because in the morning Jesus seems to pull from a large group those whom He desires to be in the inner group of twelve.
Luke 9:18 says, "Once when Jesus was praying in private and His disciples were with Him, he asked them, 'Who do the crowds say I am?'" This is a probing question, meant to be followed by the next question Jesus asked, "'Who do you say I am?'" Again, we can only speculate here about the content of Jesus' prayer, but my educated guess is on Jesus asking Father God - If this is the right time to reveal who I am [your Son] to any of the disciples then please reveal me to them Father. I guess this type of prayer because of the two questions that Christ asked and the answer that Peter gave - "Peter answered, 'The Christ of God.'" (Luke 9:20).
Here is an interesting observation - Luke 9:28-29 portrays Jesus, Peter, James and John all on the mountain praying when The Transfiguration of Jesus occurred. Matthew and Mark do not record any prayer, just the rest of the event.
"Jesus said, 'Father, forgive them, for they do not know what they are doing.'" (Luke 23:34) When? Right after the soldiers crucified Jesus. Where? At a place called, The Skull. Application: Because Jesus administered forgiveness even at the point of dying, we too can GIVE forgiveness at this point in our lives. We should not wait this long to give forgiveness and/or receive it, but it is available to give and receive until the curtain falls on this chapter of life, after that there is judgment (Hebrews 9:27).
Another example of Jesus crying out to Father God is found in Luke 23:46. Once again the scene is Jesus on The Cross and it says, "Jesus called out with a loud voice, 'Father, into your hands I commit my spirit.'" When? "about the sixth hour" (v.44) According to my sources, "the sixth hour" is our noon.
The first time prayer is associated with Jesus in John is 11:41-42. Here Jesus is in front of the tomb of one He loves dearly (verses 3, 5, 33, 35) four days after the death of this, His friend – Lazarus. The prayer was first one of thanksgiving – “Father, I thank you that you have heard me. I knew that you always hear me,…”. The second part of the prayer was to Justify His request – “I said this for the benefit of the people standing here, that they may believe that you sent me.’” Then God's power was displayed!
Jesus Prays for Himself (John 17:1-5) - "'Father, the time has come. Glorify your Son, that your Son may glorify you."
Jesus Prays for His Disciples (John 17:6-19) - Jesus prays for PROTECTION twice (verses 11b and 15). Jesus also prays for SANCTIFICATION of His Disciples by the Truth - Himself, The Word of God (verse 17).
Jesus Prays for All Believers (John 17:20-26) - Prays, "that all of them may be one, Father, just as you are in me and I am in you. May they also be in us SO THAT the world may believe you have sent me." (verse 21) Jesus prays a second time for "complete unity" (verse 23). Then, Jesus prays, "'Father, I want those you have given me to be with me where I am, and to see my Glory...'" (verse 24).
So, there you have it! I tried to leave the duplication of prayers in other Gospels out of the equation.
In conclusion, I found it important and refreshing to study and observe When, Where, and What My Savior Prayed. I discovered Jesus loved mountainsides as locations to pray. I noticed that "when" He prayed the time of day ranged from early morning hours all the way through to all-night hours. This meant to me that there is no set time to pray. However, whenever Jesus could get alone with Father God, He took the opportunity no matter when it was during the day. I uncovered "what" Jesus prayed. He prayed for children, Himself, His disciples, all Believers, and people at Lazarus' tomb. He thanked Father God for food and for hearing Him. With the children He might as well have prayed, but it is not recorded He did, just that He touched them. With Himself, Jesus prayed for glorification, "cup" to be passed, and the surrender of His spirit. With His Disciples, Jesus prayed for protection, sanctification, identification (who are the twelve), and revelation (of who He was). With all Believers, Jesus prayed for unity, company in heaven, and forgiveness. With the people at Lazarus' tomb, Jesus prayed for the power of God to be displayed for the benefit of the people standing there.
Now, it is our turn. We had and have awesome men and women of prayer in the Body of Christ. We can pull from these resources and learn from them the discipline of a strong and mighty prayer life. However, let us not forget the Biblical men and women of faith and prayer that we can observe and glean some understanding from like Paul. And let us try to soak up as much as possible all we can learn from in our ultimate example of a life full of prayer - Jesus'.