The best way to discuss Austen's use of humor and irony would be to name a couple of different examples. Although, it should be noted that when looking at Austen, it is often difficult to treat humor and irony separately since for the most part she uses irony to create her humor.
We can certainly see many examples of Austen's humor in the character Elizabeth due to her quick tongue and ready wit. One of the best examples of Elizabeth's wit takes place the time she stays at Netherfield to look after her sick sister Jane. One evening while Miss Bingley is playing lively Scottish music on the piano, Darcy turns to Elizabeth and asks if she feels like dancing a reel. Elizabeth gives a very witty reply with the intention of making Darcy look like a fool in his pride when she responds by saying he only asked her that so he could insult her taste and, therefore, will not permit him to do so, as we see in her lines:
You wanted me, I know, to say "Yes," that you might have the pleasure of despising my taste; but I always delight in overthrowing those kind of schemes ... I have therefore made up my mind to tell you that I do not want to dance a reel at all--and now despise me if you dare. (Ch. 10)
Not only are these lines witty, they can also be seen as an example of verbal irony. Verbal irony is when the speaker says the exact opposite of what he/she means, often sarcastically. These lines are most definitely spoken with sarcasm. Not only that, it's probably untrue that Elizabeth does not want to dance a reel; she would probably very much enjoy dancing a reel, but is only saying what she says to insult Darcy.
Another example of Austen using verbal irony to create humor can be seen in the very opening lines of the book:
It is a truth universally acknowledged, that a single man in possession of a good fortune must be in want of a wife. (Ch. 1)
This example of verbal irony applies to the narrator as it is the narrator who is speaking sarcastically. The irony is that it is only mothers and daughters who believe a wealthy man "must be in want of a wife." The men themselves probably give it little consideration, preferring instead to enjoy their freedom and their wealth by themselves. Therefore, the opening line does not state a "universally acknowledged truth" at all, but rather a notion held by mothers and daughters. Hence, the opening line says the exact opposite of what the author/narrator really means.