“Go, therefore, and make disciples of all nations, baptizing them in the name of the Father, and of the Son, and of the Holy Spirit.”
Our dear Savior has commissioned the Church to make disciples.  This is accomplished especially by baptism. 

As we know, baptism is absolutely necessary for salvation and must be obtained whether in fact or in desire (explicitly or implicitly) in order to have eternal life in God.  “He that believes and is baptized shall be saved, but he that believes not shall be condemned.” (Mk 16,16); “Unless a man be born again of water and the Holy Spirit, he cannot enter into the kingdom of heaven.” (Jn 3:5)

Normally, baptism is conferred by a delegated cleric of the Church i.e, a priest or deacon.  So important, however, is this sacrament, that the Church allows anyone to baptize, Christian or non-Christian, in danger of death which is done by supplying the right matter, form, and intention.
  
The matter for baptism is natural water.  That substance which is judged by the common estimation of men to be “water” is the proper matter for the sacrament.  Not beer, not weak tea; but plain old water, salt or fresh, muddy or clear; from the garden house, the Trinity River, or the neighbor’s bird bath.

The form of baptism are the words,  “I baptize you in the name of the Father, and of the Son, and of the Holy Spirit.  Amen.”  (Ego te baptizo, in nomine Patris, et Filii, and Spiritus Sancti. Amen.”)

The intention of baptism is simply the disposition, “I intend to do what the Church wants done.”  It is that broad.  Although it is preferable, the person baptizing need not have the explicit intention  to make the un-baptized a child of God but merely “to do what the Church wants done.”

How is a person baptized?
One person alone must give the whole sacrament.  The water - however applied (immersion, sprinkling, pouring) - must touch and flow over the person (living water) while saying the words, “N. I baptize you in the name of...” .

Two people may not baptize the same person.  At a Catholic Parish in Quebec, between 1991 and 1996, 295 baptisms were invalidly given.   Wherein one person alone should have conferred the sacrament, instead - and for the desire to include more people in active participation - the priest or the parent poured the water while an appointed lay person recited, “I baptize you...”
No one noticed the error until a sharp eyed grandmother - who remembered her Baltimore Catechism - voiced a complaint.  The case was investigated and the children were notified so that they might return and be validly baptized.  About 100 hundred children could not be located.

 Nor may one baptize himself.   In 1206, the Bishop of Metz saw fit to judge a case wherein a Jew, living only among Jews but greatly desiring to be baptized, baptized himself: “We respond that, since there should be a distinction between the one baptizing and the one baptized, as is clearly gathered from the words of the Lord, when He says to the Apostles, “Go baptize all nations in the name of etc.”, the Jew mentioned must be baptized again by another, so that it may be shown that he who is baptized is one person, and he who baptizes another...”

By the way, in this same letter, baptism of desire is touched upon, “If, however, such a one had died immediately, he would have rushed to his heavenly home without delay because of the faith of the sacrament, although not because of the sacrament of faith.” (DZ 413).

Now in most cases lay people will never baptize... unless they work in a hospital of live in a non-Christian country.  (In Nepal, locals will ask a foreign aid worker to baptize them; but these requests have to be tested.  Many times people want to be baptized not for reasons of salvation, but for material gain, i.e. “the rice Christian.”)  But the one place where you might baptize is in miscarriage.

I have made available the tract, “How to Baptize in Case of Miscarriage” authored in 1959 by the mother of a miscarriage.  She begins her letter by citing the 1917 Code of Canon Law, “In every case of miscarriage, no matter at what stage of pregnancy, the fetus must be baptized; absolutely, if it’s certainly alive; conditionally, if the presence of life is doubtful.”

I will leave the full reading of this letter and manner of baptism to those who are interested.

Simply know here that when the fetus leaves the mother water need be poured over the head while saying the words.  If the fetus is not sufficiently developed for this, it should be immersed in a pan of tepid water and gently swirled while reciting the words. It is important that water touch the skin of the fetus and not just the membranous sac that surrounds it. This sac must be broken to perform a valid baptism.  After breaking this sac, the fetus is placed in the pan of water and while gently swirling (living water) the reciting the baptismal form.

In the unfortunate event that a father or mother is called upon to perform such a baptism they must take consolation that their efforts are pleasing to the Savior Who told the Church in which we are her members,
“All power in heaven and on earth has been given Me.  Go, therefore, and make disciples of all nations, baptizing them in the name of the Father, and of the Son, and of the Holy Spirit...”

In such a situation, when they baptize their child, the parents have done everything they could to help their children to heaven... and they must leave the rest to the mercy of God.