Two ancient writers describe a sign said to have been given to Constantine before the battle of the Milvian Bridge in October 312, and they do not describe the same thing. Lactantius, writing within a few years of the event, reports a dream in which the emperor was told to mark a heavenly sign on his soldiers' shields. Eusebius of Caesarea, writing much later and saying he had it from the emperor himself under oath, reports a cross of light seen in the sky above the sun by the whole army, followed only afterwards by a dream. The two accounts differ in medium, in audience and in date, and the honest position is that they cannot be reconciled into a single event.
What followed is not in doubt. Maxentius was defeated and drowned, Constantine entered Rome, and within months he and Licinius met at Milan and settled a policy of open toleration. The document usually called the Edict of Milan is not an edict and was not issued at Milan: it survives as a rescript published afterwards at Nicomedia, preserved in Latin by Lactantius and in Greek by Eusebius. It granted Christians and everyone else the free exercise of their religion and ordered the restitution of confiscated church property, at public expense where the property had passed to a private buyer.
It did not make Christianity the religion of the empire. That step belongs to Theodosius I in 380. What it did was end persecution as a legal instrument and put imperial money, imperial land and imperial favour behind an institution that had spent the previous decade being dismantled.