I would like to thank Earwen for asking a question on Saint Dominic; because it caused me to do some research and I found out that I was wrong in my information. Our belief that Mary appeared to St. Dominic is based on tradition. So, this article should clear up my mistake:
Of the many forms of devotion to Our Lady, there are some which have been especially recommended by the Church. Devotions which involve the use of physical objects are not superstitious, because these objects are not thought to have any power in themselves. Rather, they are external aids to interior devotion to the Mother of God.
An especially great Marian devotion is the Rosary. There is an ancient tradition that St. Dominic received the Rosary from Our Lady in an apparition at Prouille in 1206 A.D. as a weapon against the Albigensian heresy. What is entirely certain is that in one way or another, numerous Popes have spoken of St. Dominic as author of the Rosary, without pronouncing on the authenticity of the Prouille vision. They have strongly recommended the Rosary. Vatican II in its Constitution on the Church # 67 wrote that whatever the Church has ever recommended in Marian devotion should still be considered of great importance. Not long after, Pope Paul VI in his Encyclical Christi Matris Rosarii pointed out that that statement obviously included the Rosary. Countless are the favors individuals have experienced through the Rosary. The whole Church benefited especially when in October 1571, Pope St. Pius V announced that the Christian fleet had won a decisive victory over the Muslim fleet at Lepanto in the Gulf of Corinth. The Muslims were trying to take over all Europe. The Pope explicitly attributed that victory to Rosary processions being held the day of the victory; in addition, every man on the Christian flagship had been given a Rosary before the battle. Our Lady at Lourdes and at Fatima called for a great increase in the prayer of the Rosary, declaring it one of the conditions needed for world peace and the conversion of Russia.
Okay, now that I have that cleared up, I would like to address her original question: How was it proven that Saint Dominic appeared.
Well, to begin with, it was Mary that appeared to St. Dominic. Secondly…….there is a lot of information. ;)
In order to understand how the Church has the authority to say that an apparition is authentic and be sure that they aren’t wrong (Papal Infallibility) can be read here: http://www.ewtn.com/faith/teachings/papac2.htm
And to understand how the Church decides if an apparition or private revelation is authentic can be read here: "Apparitions/Private Revelations"
Have fun reading!!