St. Cyril of Jerusalem, c.315-386

March 18 is the memorial for St. Cyril, "Famous as a teacher and preacher, he has left a series of catechetical instructions that constitute a priceless heirloom from Christian antiquity. Of the twenty-four extant discourses, nineteen were directed to catechumens during Lent as a preparation for baptism, while five so-called mystagogical instructions were given during Easter time to make the mysteries of Christianity better known to those already baptized."

Catholic Culture : Liturgical Year

His writings show the great care the early church took in the instruction and training of converts before admitting them to baptism.

Additional sources with excerpts from his instructions.

Baptism by immersion

I don't remember exactly when I was baptised--it was either 1950 or 1951, at the Church of the Brethren on Seminary Ave. in Mt. Morris, Illinois. But I clearly remember the event, and the six weeks of study with Rev. Statler that preceded it, because we lived in another town and it meant a Sunday afternoon drive. But I didn't know this about immersion baptism:

"The plunging of an adult or an infant into the baptismal font three times is the most important moment in the baptismal ceremony, and meant to be the most moving one as well. Most of us understand that this action is associated with the Trinity. It is. But the more ancient association is with the three days Jesus lay in the tomb. This is one reason why the Church now encourages candidates for baptism to be fully immersed wherever practicable. The sprinkling of water over a catechumen's head just doesn't capture the drama which the ritual intends. But when we see a person take a breath, plunge under the water, and come up for air three times, we can powerfully see the identification between Jesus' time in the tomb and the person rising to new life in Christ."

This is from a blog at a Roman Catholic site, America, the National Catholic Weekly. There is content from the print issue, and then there is on-line only material, which is where I found the link to the two blogs, one on preaching and one by editorial staff and contributors.