First lets look at passages from the Apostles teachings before we actually look at the Words of Christ Himself. First lets look at what the apostle Paul taught in Titus 2:13 "looking for the blessed hope and the appearing of the glory of our great God and Savior, Christ Jesus," in Acts 20:28 Paul address the Ephesian elders as he said "Be on guard for yourselves and for all the flock, among which the Holy Spirit has made you overseers, to shepherd the church of God which He purchased with His own blood."
The apostle Peter also taught the Deity of Christ in 2 Peter 1:1 "Simon Peter, a bond-servant and apostle of Jesus Christ, To those who have received a faith of the same kind as ours, by the righteousness of our God and Savior, Jesus Christ:"
The apostle John makes the claim of Jesus' Deity right in the first chapter of his gospel in John 1:1 "In the beginning was the Word, and the Word was with God, and the Word was God." and then 13 verses later in John 1:14 he says Jesus is the Word, "And the Word became flesh, and dwelt among us, and we saw His glory, glory as of the only begotten from the Father, full of grace and truth."
The apostle Thomas makes the most direct claim of the Deity of Christ in John 20:28 said "My Lord and my God!". There are numerous text which the apostle's clearly make the claim of Christ's Deity but I think it's fair to say that from these four apostle's we just mentioned the teaching of the Deity of Christ was widely accepted among all the apostle's.
Now let's look at the claims of Christ Himself and see what he actually taught about Himself.
1. Jesus is Omnipresent:
Matthew 28:20 "teaching them to observe all that I commanded you; and lo, I am with you always, even to the end of the age." and also in Matthew 18:20 "For where two or three have gathered together in My Name, there I am in their midst"
2. Jesus is Omnipotent and Sovereign:
Matthew 20:18 "And Jesus came up and spoke to them, saying, All authority has been given to Me in heaven and on earth." Jesus said He has the power to forgive sins Matthew 9:6 "But so that you may know that the Son of Man has authority on earth to forgive sins...." Then he said to the paralytic, "Get up, take your mat and go home." Jesus also claimed to have the power to give eternal life in John 17:2 He said "even as You gave Him authority over all flesh, that to all whom You have given Him, He may give eternal life." In Luke 8:25 Christ demonstrated His power over creation "And He said to them, "Where is your faith?" They were fearful and amazed, saying to one another, "Who then is this, that He commands even the winds and the water, and they obey Him?"
3. Jesus is Omniscience:
Matthew 26:21 "And while they were eating, he said, "I tell you the truth, one of you will betray me." and in John 2:24-25 "But Jesus, on His part, was not entrusting Himself to them, for He knew all men, and because He did not need anyone to testify concerning man, for He Himself knew what was in man." and also in Luke 6:8 "But He knew what they were thinking, and He said to the man with the withered hand, "Get up and come forward!" And he got up and came forward." Now there are many other passages that affirm the Omniscience of Christ as Thomas Schultz observes that:
The knowledge of Christ is far beyond any mortal knowledge. He is not just a genius, not just the wisest of all humans. His wisdom far exceeds all human limitations and could only be classified as perfect knowledge. First, He knows the inward thoughts and memories of man, an ability peculiar to God (1 Kings 8:39; Jeremiah 17:9-16). He saw the evil in the hearts of the scribes (Matthew 9:4), He knew beforehand those who would reject Him (John 10:64) and those who would follow Him (John 10:14). He could read the hearts of every man and woman (Mark 2:8; John 1:48; 2:24, 25; 4:16-19; Acts 1:24; 1 Corinthians 4:5; Revelation 2:18-23). A mere human can no more than make an intelligent guess as to what is in the hearts and minds of others. Second, Christ has a knowledge of other facts beyond the possible comprehension of any man. He knew just where the fish were in the water (Luke 5:4-6; John 21:6-11), and He knew just which fish contained the coin (Matthew 17:27). He knew future events (John 11:11; 18:4), details that would be encountered (Matthew 21:2-4), and He knew that Lazarus had died (John 11:14). Third, He possessed an inner knowledge of the Godhead showing the closest possible communion with God as well as perfect knowledge. He knows the Father as the Father knows Him (Matthew 11:27; John 7:29; 8:55; 10:15; 17:25). The fourth and consummating teaching of Scripture along this line is that Christ knows all things (John 16:30; 21:17), and that in Him are hidden all the treasures of wisdom and knowledge (Colossians 2:3).
Jesus is Everlasting:
Now I want to present just one last proof that the scripture teaches the Deity of Christ in that He claimed to be Eternal which is found in John chapter 8 beginning with verse 56 where He tells the Jews "Your father Abraham rejoiced to see My day, and he saw it and was glad." So the Jews said to Him, "You are not yet fifty years old, and have You seen Abraham?"Jesus said to them, "Truly, truly, I say to you, before Abraham was born, I am." Therefore they picked up stones to throw at Him, but Jesus hid Himself and went out of the temple." You see you may not get what Jesus said to the Jews but they got it and that's why the tried to kill Him johnny on the spot.
Now to claim to be Everlasting, Omnipresent, Omnipotent and Omniscience is equivalent to saying "I am God". But Christ did more than just claim to be God, He revealed to us in fact that He is God.