Did Jesus pray to God according to the prevalent Jewish customs? How did he pray to God? What does the Gospel say about it?
Indeed, Jesus did prayer to his Father, as His Father.
“Father, the hour has come. Glorify your Son, that your Son may glorify you. For you granted him authority over all people that he might give eternal life to all those you have given him. Now this is eternal life: that they know you, the only true God, and Jesus Christ, whom you have sent. I have brought you glory on earth by finishing the work you gave me to do. And now, Father, glorify me in your presence with the glory I had with you before the world began.
In this instance, while it may sound like he is "puffing himself" up, it is to be remembered that Jesus and His Father were one. As he says in John 10:28-30 "I give them eternal life, and they shall never perish; no one will snatch them out of my hand. My Father, who has given them to me, is greater than all; no one can snatch them out of my Father’s hand. I and the Father are one." Thus, by glorifying himself, he glorifies the Father, since they are one.
“And when you pray, do not be like the hypocrites, for they love to pray standing in the synagogues and on the street corners to be seen by others. Truly I tell you, they have received their reward in full. But when you pray, go into your room, close the door and pray to your Father, who is unseen. Then your Father, who sees what is done in secret, will reward you. And when you pray, do not keep on babbling like pagans, for they think they will be heard because of their many words. Do not be like them, for your Father knows what you need before you ask him.
“This, then, is how you should pray:
“‘Our Father in heaven, hallowed be your name, your kingdom come, your will be done, on earth as it is in heaven. Give us today our daily bread. And forgive us our debts, as we also have forgiven our debtors. And lead us not into temptation, but deliver us from the evil one.’
Jesus is calling for a very personal approach to prayer here. He calls God Father, and instructs us to do the same.
There are many, many other examples, as this link shows.
Jesus prayed for others. In Matthew 19:13, we read, "Then little children were brought to Jesus for him to place his hands on them and pray for them." Despite the fact that "the disciples rebuked those who brought them," Jesus said the children should not be hindered "for the kingdom of heaven belongs to such as these" (v. 14). In John 17:9 we read, "I [Jesus] pray for them. I am not praying for the world, but for those you have given Me, for they are Yours." This underscores the need for intercessory prayer.
Jesus prayed with others. Luke 9:28 reads, "[Jesus] took Peter, John and James with Him and went up onto a mountain to pray." Jesus prayed alone, as we'll read below, but He also knew the value of praying with others. Acts 1:14 underscores the importance of Christians praying with one another: "They all joined together constantly in prayer …"
Jesus prayed alone. Luke 5:16 reads, "But Jesus often withdrew to lonely places and prayed." As much as Jesus understood the value of praying with and for others, He also understood the need to pray alone. Psalm 46:10 reads, "Be still, and know that I am God." Sometimes it's important for us to "be still" before God, but the only way to do this, especially in our hectic culture, is to do so alone with God.)
During many times in His life, Jesus withdrew from His disciples and the crowds, to be alone to pray. He often went up on a mountainside or went to solitary or lonely places to pray. Sometimes He even went to pray very early in the morning, while it was still dark (Matthew 14:23, Mark 1:35, 6:46, Luke 5:16).
The eternal Father and the eternal Son had an eternal relationship before Jesus took upon Himself the form of a man. In John 5:19-27, we get to know this relationship where Jesus says that “whatever the Father does, the Son does likewise.” Particularly in verse 23 He says:
John 5:23 So that all people will honor the Son just as they honor the Father. The one who does not honor the Son does not honor the Father who sent him.
Jesus taught that He and His Father are one (John 10:30), meaning that He and His Father are of the same substance and the same essence.
Jesus, the eternal Son of God, took upon Himself sinless humanity, giving up His heavenly glory (Philippians 2:5-11). Jesus was both God and man in one person. For this reason we see His tempting by Satan (Matt. 4:1-11), accused falsely by men, rejected by His people, and eventually crucified. He had a will. He ate. He slept, etc.
He was a man. He needed to be a human in order to bear the sins of people. He needed to be God in order to offer a sacrifice to God the Father sufficient to cleanse us of our sins. No mere man could do this. But the fact is, Jesus was one person -- and still is. Jesus was both God and man at the same time in the form of a single person. It is, therefore, not surprising that Christ did what every God-fearing person is supposed to do, namely pray to God.
In John 17, from verse 1 to 5 Jesus prays to God to glorify him by completing the works that he was to fulfil for the salvation of humanity by dying on the cross though he was God. In the second part from verse 6 to 19 he prays for his disciples. And lastly from verse 20 to 26 he prays for all the humanity.
In this full chapter of John 17, we see that whatever he was communing with his Father was like a conversation. It is the Son of God in His humanity talking with God the Father, two parts of the tri-unity, along with the Holy Spirit, the Father God, the Son God, and the Spirit God, not three gods, but one God existing as three persons.
Yes he did, as a son would, there was many time in the gospels were Jesus would leave his followers and spend time alone with God. There were times when Jesus fasted and prayed "Luke 6;12" Jesus went into the mountain area to pray and he spent the whole night in prayer to God.