I see that Free has given an explanation. I will just simply post a few scriptures that, to me, support the Trinity:
"And Jesus, when he was baptized, went up straightway out of the water: and, lo, the heavens were opened unto him, and he saw the Spirit of God descending like a dove, and lighting upon him:
And lo a voice from heaven, saying, This is my beloved Son, in whom I am well pleased". (Matt. 3:16,17)
The verse above is in direct contrast to those who would say that God has "revealed Himself in three different ways". (modalism) We see clearly here that all (3) persons of the Trinity are present at ONE TIME. There is the SON of God being baptized, the Holy Spirit descending, and A VOICE from Heaven which states "this is my beloved Son".
"Go ye therefore, and teach all nations, baptizing them in the name of the Father, and of the Son, and of the Holy Ghost" (Matt. 28:19).
This is very clear also---people are to be baptized in the name of ALL THREE at one time. You don't get baptized separately under the Father, or under the Son or Spirit---no--it is "in the name of the Father, Son and Spirit at one time. That is because these three persons are ONE GOD.
"Above it stood the seraphims: each one had six wings; with twain he covered his face, and with twain he covered his feet, and with twain he did fly.
"And one cried unto another, and said, Holy, holy, holy, is the Lord of hosts: the whole earth is full of his glory". (Isaiah 6:2,3)
Though this is no definitive "proof" I have always found it interesting, and actually amazing too that these Seraphim shout: "HOLY, HOLY, HOLY is the Lord of Hosts". Why not two times, or four? God has created these beings to glorify Him. Why create them to say this phrase (3) times over and over?