Satire is used to treat the topic of marriage through the ironic and trivial nature of the dialogues that occur between:
Lady Bracknell and Jack
Gwendolen and Jack
Algernon and Jack
Cecily and Algernon
In all, the four main characters as well as Lady Bracknell all share a ridiculous idea of marriage that makes up for the satire of the story.
For example, when Lady Bracknell speaks to Jack about the prospects of a marriage to Gwendolen, she takes out a notebook in which she has already written specific questions. This shows that she pesters every man that attempts to come near Gwendolen with a long list of questions that, like she says, she works with "in a team" with "the Duchess".
Furthermore, she openly criticizes the answers that she gets and is more than happy to insult whatever she does not like. This is the case when she not only calls Jack's lineage "a parcel", but she also obligates him to produce a family name immediately or "before the season is over". The shallowness and meanness of the woman are so extreme that the reader has no other choice but to realize the irony and laugh at its shocking nature. Hence, marriage is a contract that better bring good outcome. This is the view of Lady Bracknell.
Gwendolen, although not as mean as her mother, has another weird view of marriage which, in another ironic comedy, she shares with Cecily (unknown to both): They both insist in marrying a man named Ernest. Period. They both love the name because it insinuates itself as if whoever wears the name is a good and honest man. To Gwendolen, the name brings "vibrations". To Cecily, it implies a hidden mischievous behavior that she intends to modify. The two women are so far out in their views of marriage that, again, we find no other option but to laugh at them and their views.
Finally, Algernon and Jack also share their views. Algernon does not care and also thinks of marriage as a business transaction. This, however, miraculously changes after he meets Cecily. However, he has already been planning on romancing Cecily even before he meets her. This shows, once again, that Algernon is a creature of whims and Cecily is nothing but a caprice. This is no different that Cecily's opinion of Algernon (whom she thinks is Jack's bad brother Ernest). They are both clueless.
As for Jack, he is the only character who seems to be genuinely in love. He endures Lady Bracknell's insults and Algernon's comments, all for the sake of Gwendolen. He is willing to go get baptized as an Ernest, and goes through the tribulations of the play for her. However, Jack has a tendency to lead a double life. He even admits to being in shock to have been telling the truth about his name all this time. Jack is also weak in the flesh. He leads us to assume that he, too, will break vows.
In call, none of the characters has a good nor healthy vision of what a good marriage is, and this is how Wilde uses satire to treat the topic.