What document tells of Constantine's vision and did this truly lead Christinity to victory?
Constantine did claim to have seen a vision of the Cross, and told his soldiers to carry the symbol on their shields at the battle of Milvian Bridge; however the sincerity of Constantine's conversion and his motives for convening the Council of Nicaea are subject to some debate.
At the time of Constantine's "vision," no one was present other than himself. Interestingly, Christianity was a growing force in the Empire, and previous attempts by Diocletian and other Emperors to eradicate it had failed miserably. There is some argument that Constantine's position amounted to "if you can't beat them, join them." He never shared the story of his vision with anyone until he was on his deathbed, at which time he was baptized as a Christian. He apparently wished to avoid repentance as long as possible. His favoritism of Christianity did not stop him from murdering his wife and having his son executed on the trumped up charge that he had seduced his step-mother.
Constantine did seem to be a man of vision, or "visions." He had another vision in which he saw an old woman who became young again while visiting the ancient city of Byzantium. He used this vision as his justification to move the Roman capital to Byzantium which he later named for himself: Constantinople. One is left to conclude that the geographic advantages of the city on the Straits of Bosphorus were not part of his consideration.
As for the Council of Nicaea, Constantine's real motive was to resolve an inter-Christian dispute over the divinity of Christ due to the growing converts to Arian Christianity, which held that Jesus was human but not divine. The council determined that Jesus was both human and divine, and Arianism was condemned as heresy, but later in his reign, when Arius' preaching seemed to predominate, Constantine shifted his support to that interpretation. Only after the death of Arius and the traditional belief prevailed was Arianism once again prevalent. So one must conclude that Constantine was pragmatic, if not opportunist.
A final element of Constantine's ambiguous beliefs should be considered. Before his first vision, he had been a sun worshiper. The sun god was known as Sol Invictus, (the unconquered sun.) It is no coincidence that Christians soon adopted their day of worship as Sunday.
An excellent discussion of Constantine and his motives can be found in Lars Brownworth's Lost to the West.
The main sources for the conversion of Constantine is Eusebius and Lactantius. They both write of Constantine's vision of the chi-rho, which are the first two letters of Christ in Greek. They also mention that Constantine heard a voice say: "in hoc signo vinces," (in this sign you will win).
As for the significance of this event, it cannot be underestimated. This stopped the persecutions against Christianity. For example, in 313 the Edict of Milan was passed, which allowed Christianity to worship without persecution. In addition, Constantine began to favor Christianity. For example he called the council of Nicaea in 323 where the deity of Christ was the topic. He even saw himself as the 13th apostle. These religious benefits were a huge help in establishing Christianity in the ancient world.