Jesus Christ came to save all people, and told the Church to preach the Gospel to all nations, 'baptizing them in the name of the Father, and of the Son, and of the Holy Spirit, teaching them all that I have commanded you.' (Matthew 18b-19a).
Therefore, all over the age of 7 may be baptized if they sincerely ask for baptism, intend to live a Catholic life, and have not previously been baptized. Usually, there is a period of instruction in the faith. This instruction is called catechesis (same root as the word catechism). The Rite of Christian Initiation of Adults (RCIA) is the usual process of catechesis. Individuals who have participated in the RCIA are usually baptized at the Easter Vigil. Right after their baptism, they are confirmed, and then receive Holy Communion for the first time.
The Church does not 'rebaptize' anyone. If a person has been validly baptized in another Christian community, the Catholic Church recognizes that baptism. Such persons become Catholic by making a public profession of faith that they believe all that the Catholic Church believes and professes as having been revealed by God.
For children younger than 7, the parents or legal guardians must ask for the baptism of the child. A child may not be baptized against the wishes of the parents or legal guardians. A priest may delay the baptism of a child if he believes that he/she is unlikely to be raised in the Catholic faith.
Of course, in danger of death, there is no time for catechesis, and a person should be baptized immediately. All too often, the priests at St. John's are called upon to baptize sick newborns. In an emergency, when no priest of deacon is available, anyone can perform a baptism by pouring ordinary water over the head of the person while saying the words: 'I baptize you in the name of the Father, and of the Son, and of the Holy Spirit.'