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This looks like a job for... Canon Law 869
Can. 869 Β§1. If there is a doubt whether a person has been baptized or whether baptism was conferred validly and the doubt remains after a serious investigation, baptism is to be conferred conditionally.
Β§2. Those baptized in a non-Catholic ecclesial community must not be baptized conditionally unless, after an examination of the matter and the form of the words used in the conferral of baptism and a consideration of the intention of the baptized adult and the minister of the baptism, a serious reason exists to doubt the validity of the baptism.
The gist of it is, there's no need for re-baptism, being baptized by anyone in the name of the Father and of the Son and of the Holy Spirit is sufficient.
And in time of need, it is valid for anyone to baptize anyone else. For instance, if you were in a really bad accident and I came upon you and said, "boy, you look pretty rough are you ready to meet the Lord" and you said, "Lord who?" and I, while dressing the wounds of your mangled body, managed to convince you of the truths of the Catholic Church and you decided that you wanted to die a Christian, I could baptize you and even if you managed to live, you wouldn't need to be re-baptized.
The requirements for joining the Church are different for unbaptized folks than for baptized. Either way, the RCIA process is followed and culminates with all three sacraments of initiation Baptism, Eucharist and Confirmation (with the exception of Baptism for the already Baptized) .
The liturgical part of the process can be found in this book I bought it and read through it because I'd like my dad to become Catholic, but it's not much help really.
What one would need to do in order to become convert to Catholicism, would be largely up to the priest. I have a friend who is a convert who showed up on a priests doorstep 30 some years ago and the priest gave him one-on-one instruction until he joined the church. But others, Lutherans in particular, say "all the priest said to do was make a general confession", other parishes have RCIA programs led by lay ministers similar to Catechetical instruction for children leading up to their confirmation.