Anyone man or woman, a child who has reached the age of reason can baptize. To do so the requirements are as follows. If the person being baptized is below the age of reason, they are baptized with potable water, and as the water is poured, sprinkled or they are immersed, the person preforming the action says, I baptize thee in the Name of the Father, and of the Son and of the Holy Ghost, (Spirit). The person baptizing needs to simply attempt to do what the Church intends or if they are a non-Christian or non-baptized person who claims to be a Christian, do what Christians hold sacred. As the primary minister in all the Sacraments is Christ Jesus, the faith of the minister is not essential. If the person has reached the age of reason, then they must manifest faith in Christ, and have asked to be baptized.
If there is question as to if a valid baptism has been preformed before or if the person showed interest in baptism and cannot speak now, (a person in a coma etc.) They can be baptized conditionally, you simply add to the beginning of the words of baptism, If you are not baptized. If the person who has reached the age of reason would not have wished to be baptized, it is not a magical rite like the pagan rites, so they are not baptized. That however is usally known only to God and the soul of the person when they meet Him at Judgement.