It clearly says in the Old Testament, that God is one : "Hear, O Israel: the LORD our God, the LORD is one" Deuteronomy 6:4, so how come the New Testament contradicts the Old Testament by saying God is three in one, no where in the Old Testament does it mention that God is three in one
How Can God Be A Trinity
The doctrine of trinity is not specifically taught in the Bible. It is a derived doctrine from verses that mention the Holy Spirit is sent by the Father and Jesus and verses that describe the Holy Spirit as God as well. Not all Christians subscribe to the trinity, however most do.
In the verse you cite in Deuteronomy the word “one” is 'echâd which emphasizes unity. The word God is 'ĕlôhı̂ym and is plural.
The Bible shows us true things about God. One problem we have is that we often think we understand more than we do. Much argument and dissention stems from those who do not have humble hearts but want to advance their own ideas.
If we are perplexed by the Bible that describes a plurality as well as a unity in regard to God, we may desire to resolve this by picking one and fighting those who have picked another aspect. It takes a humble heart to say, “I do not fully understand this and will treat it as a mystery”.
God revealed himself to Moses as "I am" in Exodus. Jesus revealed himself to his disciples as the "Son of Man" and "Son of God", as worthy of worship and equality with God, often (as in John's gospel) by using "I am" statements: "I am the bread of life", "I am the resurrection and the life", "I am the way, the truth and the light". The Holy Spirit was revealed by Jesus and through its (His?) actions and through the knowledge imparted to the writers of scripture. As Jesus said when talking to Nicodemus in John 3:
5 Jesus answered, “Very truly I tell you, no one can enter the kingdom of God unless they are born of water and the Spirit. 6 Flesh gives birth to flesh, but the Spirit[b] gives birth to spirit. 7 You should not be surprised at my saying, ‘You[c] must be born again.’ 8 The wind blows wherever it pleases. You hear its sound, but you cannot tell where it comes from or where it is going. So it is with everyone born of the Spirit.”
The working of the Spirit is a mystery. In Colossians 1:27:
To them God has chosen to make known among the Gentiles the glorious riches of this mystery, which is Christ in you, the hope of glory.
I will not argue the "whether" of the trinity, but the "how". The Bible never answers the "how" question. God just is and always has been. He is as he is and not some other God. There is no cause for him, no "how" that can be given.