As a practical matter, there is a process in place in every Catholic parish, known as Rite of Christian Initiation of Adults. A similar pattern is followed by returning Catholics, so called reverts.
I went through it — I was an unchurched and uncatechized Orthodox since infancy.
It normally starts in the fall, continues through the winter and spring and if all goes smoothly, culminates with acceptance to the Church at Easter.
I hasten to emphasize that this is not a firm calendaric requirement. For good reason, speedier arrangements can be made. One in danger of proximate death should speak to the priest immediately and he, if sincere, will be received as speedily as his physical condition or risks demand. Many conversions happen literally at the hour of death.
But ordinarily, that is the schedule. If you are interested, and not — we hope — in a hurry, wait till September and ask in the parishes near you. Shop around: given the infestation of liberalism in the Church, it is very worthwhile to make sure solid doctrine is taught in the RCIA. It tends to be manned, or womanned, by rather liberal nuns, and, naturally, the Church wants to be receptive to anyone and that often adds to the liberalism, and subtracts from orthodoxy.
Remember that the Catholic Church has Eastern Particular Churches alongside the better-known Latin Rite, that are Eastern Orthodox in character; you are free to choose any of these, so long as they are in communion with Rome. They are known as Byzantine Rite, Ukrainian, Ruthenian, Melkite, Greek Catholic, Maronite and several others. You can enter through one such Church and practice in another, as well as switch between such Churches (also confusingly called Rites) pretty much at any time and multiple times. Be warned though that the Office of the Readings and some lesser holidays do not always match.
The process is broken down in two stages, Inquiry and Catechumenate. Inquiry is very informal, people come and go, it is there to have your questions posed and answered. If following the Inquiry a serious interest is felt, the Catechumenate will express his desire to enter the Church. He will be required to attend Mass, if at all possible, at the hour when his catechumenate class is held, and at Church holidays (Catholic churches often have several Masses on Sunday, but the Mass at which the Catecumens are asked to be present will likely be the late morning Mass). There are, at that stage, certain prayers and blessings that the Church will say for you and you will be dismissed for class ceremoniously lead by the Bible held high, to a class room as a hymn is sung and the congregation begins the Eucharist. In other words, you participate in the Liturgy of the Word, but are sent off to class right before the Eucharist. The classes become more structured, you will get the basics of Christian theology and praxis. There are several non-obligatory celebrations during Lent and the Holy Week, such as the Stations of the Cross, which you will have a chance to experience. Usually, there is a weekend retreat to a monastery with more concentrated prayers, communal meals and meditations. Naturally, no committment is incurred until the sacraments of initiation are celebrated.
The sacraments that you will receive depend on the sacraments already received. Generally, the Protestant baptisms are considered valid. If there is a doubt, a conditional baptism is scheduled, but if there is evidence of a baptism with water using the full Trinitarian formula, you will not be baptized nor conditionally baptized. You will also be confirmed (as far as I know, Catholic confirmation is always done, even if something similar was celebrated in your prior denomination). If you wish, you can go to first confession right then, although confession is always on your own initiative in the Church. You will be asked to swear an oath publicly in front of the congregation, — I quote closely from memory, — “I believe that all that the Catholic Church teaches, professes and proclaims was revealed by God”. Do not be surprised if and some point the congregation will stand up and give you a so-incorrectly-called Nazi salute.
Confirmation will be celebrated in the Cathedral and you will be chrysmated by the Bishop.
The first Communion will be celebrated, normally, on the Holy Saturday at the Easter Vigil Mass.
No ecclesial status received in another denomination automatically transfers with conversion. Provisions exist for Anglican/Episcopal clergy, especially in the States.
Interestingly, Orthodox priests that switch over do not have special provisions even though they are valid priests right where they are. Protestant clergy especially often finds themselves in a difficult position after conversion, as they typically struggle to define for themselves some lay ministry compatible with their talent and training. A good networking tool for people in that position is Marcus Grodi with his Coming Home Network.
All, despite difficulties, at times severe, should come home where you all belong. You will never see the same person in the mirror again.
You have explained RCIA very well from a personal point of view. Thank you!
**Many conversions happen literally at the hour of death.**
My priest has talked about numerous Sacraments, Anointing of the Sick, Baptism, Holy Eucharist, Confirmation (the priest is authorized in these cases to perform this Sacrament.)
He even talked about performing a valid marriage for the couple (one partner dying, of course.) It seems that even the Sacrament of Reconciliation was mentioned by him too, depending on if the person is coming back to the church — revert, as you say above.