Marriages between commoners are the equivalent of common law, with either partner able to end it by simply stating that the marriage is over at their will. Similarly, they do not need to consult with anyone to declare themselves married, and can simply inform a local seraph or lord that it has transpired to be noted for the public record, but marriage ceremonies performed by a godsworn is more common.
In both commoner and noble marriages, either the bride or groom will be 'marrying in' to the other's family, but there is no gender distinction here. Typically the family seen as 'gaining' a family member will be seen as gaining significantly in the match, with the house gaining a family member often covering wedding expenses, and for noble marriages, being seen as a major chip in marriage negotiations, with it considered a major concession that a family member is going to another house, and likely to expect treaty concessions in turn with land grants, favorable diplomatic and trade partnerships, expectations that some of the children will be wards of the former family, or the like.
For noble marriages, any match between nobles has implications before Limerance, and so requires at least the consent of the faith. For a 'love match' without any formal treaty, this requires the approval of the heads of each household and at least a local seraph. For any marriage pact that creates a formal treaty between two houses, this is theoretically approved of by the Archlector of Limerance (or his or her godsworn staff), or any legate, or the Dominus. Marriages involving a highlord tend to be seen by the dominus or one of the legates. Nobles that elope do not have their marriages recognized as legitimate in the eyes of the Faith until they have formal approval by the Faith.
It's rare for any marriage to not be approved, and theoretically it exists as a safeguard against marriage under duress, which is forbidden by the Faith of the Pantheon, to be certain that a spouse agrees to the marriage under their own free will. Of course, since heads of house can dennoble a family member that thwarts them, consent can be murky if someone is facing the threat of losing their title unless they consent to a marriage. Similarly, nobles wishing to marry commoners are typically expected to give up their noble title as a sign of commitment and join the commoner's family, unless the commoner passes a tremendously high bar to be worthy of ennoblement.