Why did God dispose man and woman for each other?
God disposed man and woman for each other so that they might be “no longer two but one” (Mt 19:6). In this way they are to live in love, be fruitful, and thus become a sign of God himself, who is nothing but overflowing love.
How does the sacrament of Matrimony come about?
The sacrament of Matrimony comes about through a promise made by a man and a woman before God and the Church, which is accepted and confirmed by God and consummated by the bodily union of the couple. Because God himself forms the bond of sacramental marriage, it is binding until the death of one of the partners.
The man and the woman mutually administer the sacrament of Matrimony. The priest or the deacon calls down God’s blessing on the couple and, furthermore, witnesses that the marriage comes about under the right circumstances and that the promise is comprehensive and is made publicly. A marriage can come about only if there is marital consent, that is, if the man and the woman enter marriage of their own free will, without fear or coercion, and if they are not prevented from marrying by other natural or ecclesiastical ties (for example, an existing marriage, a vow of celibacy). (YOUCAT questions 260 & 261)
Dig Deeper: CCC section (1601-1605) and other references here.