What is needed between two Catholics?
They would approach their priest and attend the diocesan required premarital preparation (this process varies by diocese as to what it entailed).
They would complete a premarital investigation questionnaire with the priest which includes gathing of paperwork such as baptismal records and determination of freedom to marry, impediments, etc.
They would marry in the Catholic form:
Can. 1108 §1. Only those marriages are valid which are contracted before the local ordinary, pastor, or a priest or deacon delegated by either of them, who assist, and before two witnesses according to the rules expressed in the following canons and without prejudice to the exceptions mentioned in cann. ⇒ 144, ⇒ 1112, §1, ⇒ 1116, and ⇒ 1127, §§1-2.
If you want to type more, what’s needed between a Catholic an a non-Catholic?
In addition to the above, the Catholic must apply for and recieve permission for a mixed marriage (if the other person is a baptized non-Catholic) or a dispensation from disparity of cult (if the other party is unbaptized). The priest handling the marriage preparation does this.
Additionally the Catholic will make promises regarding the rearing of the children in the Catholic faith.
Can. 1124 Without express permission of the competent authority, a marriage is prohibited between two baptized persons of whom one is baptized in the Catholic Church or received into it after baptism and has not defected from it by a formal act and the other of whom is enrolled in a Church or ecclesial community not in full communion with the Catholic Church.
Can. 1125 The local ordinary can grant a permission of this kind if there is a just and reasonable cause. He is not to grant it unless the following conditions have been fulfilled:
1/ the Catholic party is to declare that he or she is prepared to remove dangers of defecting from the faith and is to make a sincere promise to do all in his or her power so that all offspring are baptized and brought up in the Catholic Church;
2/ the other party is to be informed at an appropriate time about the promises which the Catholic party is to make, in such a way that it is certain that he or she is truly aware of the promise and obligation of the Catholic party;
3/ both parties are to be instructed about the purposes and essential properties of marriage which neither of the contracting parties is to exclude.
Can. 1086 §1. A marriage between two persons, one of whom has been baptized in the Catholic Church or received into it and has not defected from it by a formal act and the other of whom is not baptized, is invalid.
§2. A person is not to be dispensed from this impediment unless the conditions mentioned in cann. ⇒ 1125 and ⇒ 1126 have been fulfilled.
And lastly, in a mixed marriage or disparity of cult marriage, the Catholic can be dispensed from Catholic form if they had a valid reason for marrying in the non-Catholic’s place of worship.
Can. 1117 The form established above must be observed if at least one of the parties contracting marriage was baptized in the Catholic Church or received into it …] without prejudice to the prescripts of ⇒ can. 1127, §2.
Can. 1118 §1. A marriage between Catholics or between a Catholic party and a non-Catholic baptized party is to be celebrated in a parish church. It can be celebrated in another church or oratory with the permission of the local ordinary or pastor.
§2. The local ordinary can permit a marriage to be celebrated in another suitable place.
§3. A marriage between a Catholic party and a non-baptized party can be celebrated in a church or in another suitable place.