A marriage or union of matrimony was a legally or culturally recognized bond between two or more spouses. In many cultures, marriage could be celebrated through a wedding ceremony. The dissolution of a marriage was known as a divorce or annulment.
In Taresian culture, the term "joined" was used for the practice apparently coinciding with what Humans called marriage. (VOY: "Favorite Son")
Human marriages were typically between one woman and one man. (VOY: "Favorite Son") The case, however, of the Mariposans and Bringloidi, and their need for a large genetic base to survive, meant that each woman, from both groups, had to have at least three children by three different men. It also meant that monogamous marriages would not be possible for several generations. (TNG: "Up The Long Ladder")
Harry Kim's statement in "Favorite Son" that Human marriages were usually one woman with one man seems to suggest that other configurations exist, but are somewhat rare. In TNG: "Family", Louis casually remarks that he married both of the Bloom sisters, although he retained the marriage to only one of them.