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A person is brought into full communion with the Catholic Church through reception of the three sacraments of Christian initiation—Baptism, Confirmation, and the holy Eucharist—although the process by which one becomes a Catholic can take different forms.
A person who is baptized in the Catholic Church becomes a Catholic at that moment. The Sacraments of Confirmation and the Eucharist deepen one's initiation.
Those who have been validly baptized outside the Church become Catholic by making a profession of the Catholic faith and being formally received into the Church. This is normally followed by Confirmation and the Eucharist.
Before a person is ready to receive the Sacraments and/or be received into the Catholic Church, they must go through a time of preparation which depends on the individual’s circumstance. For adults and children who have reached the age of reason (age seven), entrance into the Church is guided by the Rite of Christian Initiation for Adults (RCIA). RCIA is the formation process for adults who are considering the sacraments of initiation (Baptism, Confirmation, Eucharist).
Source: Catholic.com