*Edited and improved*
Hello, and welcome to SI!
These are good questions.
These are good questions! Since the time of the Apostles men have wrestled with this subject. Finally, in the sixth century AD the issue came to a head, and resulted in an overwhelming agreement in the Church called the [url=http://www.ccel.org/creeds/athanasian.creed.html]Athanasian Creed[/url], which I suggest every Christian read.
The basic idea is that one God has and does exist from eternity in three persons, the Father, the Son, and the Spirit. Again, these three Persons are one God. They are not each 1/3 of God, or three separate Gods. They are Each and One Almighty God Indivisible. Confused? You should be. If God could be fully comprehended by men, He would be an invention of man.
We derive these truths as necessary consequences of comparing scripture to scripture. If it had not been revealed by God in the Word, we would never have guessed it. There are many available resources to show the passages and explain difficulties, such as [url=http://www.gotquestions.org/Trinity-Bible.html]this[/url] and [url=http://www.trinityfoundation.org/journal.php?id=180]this[/url], but here are two plain reasons for believing in the Trinitarian view of God.
Consider the reasoning of God in Hosea 13:4.
"I am the LORD thy God from the land of Egypt, and thou shalt know no god but me: for there is no saviour beside me."
Divine logic is direct: because God alone can decisively save men, no one else is worthy of worship. Only a capable savior may be lifted up as God, and God is the only capable Savior. Then we must relive the surprise which would have overcome first-century Jews who read in John's first epistle,
"We have seen and testify that the Father has sent his Son to be the Savior of the world." [1 John 4:14]
If the Son is a mere finite being then this privileged title would be infinitely inappropriate. He would be like the man of lawlessness, "sitting in the temple of God, showing Himself that He is God." [2 Thes. 2:4] Yet note how many times the New Testament teaches us to look to Jesus for salvation. Clearly this is an office reserved in the Old Testament to God and is suitable to Christ only if He is Himself Deity. This is His own emphatic claim, for as we read in John 8:58, Jesus spoke of Himself in the present perfect tense, as one who is eternally existent:
"Jesus said unto them, Verily, verily, I say unto you, Before Abraham was, I am."
This radical claim was acknowledged by the Pharisees who took up stones to kill Jesus for blasphemy, since this was nothing else but an assertion to be essentially one with the God of Exodus 3:14 -
"And God said unto Moses, I AM THAT I AM: and he said, Thus shalt thou say unto the children of Israel, I AM hath sent me unto you."
If we now agree that God has existed from all time in the persons of both the Father and the Son, as well as the Spirit, then we may begin to receive the fact that these persons have always shared communication amongst themselves in a way we cannot fathom, probably because of its sublime simplicity and not some humanly contrived complexity. But even if such a glorious exchange consisted in unified agreement regarding the decrees, and a wonderfully mutual love and worship of Himself, this leaves the question of why it was necessary for God the Son Incarnate to pray?
When the Son took on flesh as Jesus Christ, he came to be the Second Adam, to stand for the Elect as their legal Representative. This meant fulfilling the perfect obedience required by God of men, in order to receive for us the heavenly reward. Therefore he lived as a perfect man, made under the law and like us in all things, sin excepted [Gal. 4:4]. Though possessing two complete natures, that of God and that of true man, He was yet one person. As God He is equal to the father. As the perfect man he humbled Himself to pray. He became the supreme pattern of humility, faith, and obedience. Just as Jesus was also baptized to fulfill obedience, so He made use of prayer as God's appointed means for delivering His will, and received answers by that means. In this way Christ is a suitable High Priest for us.
With all this in mind, I suggest you read John 17 and rejoice in our great God and Savior, Jesus Christ.