The play is of course full of scenes and lines that are hilarious. What makes them hilarious is the way that Wilde blends a number of different genres of comedy within this play. For example, this play is clearly to some extent a comedy of manners, which is a comedy that critiques the social norms and conventions of the day by holding them up and showing them to be ridiculous. Note how this is achieved through Lady Bracknell's response to Algernon's news that he will not be able to attend her dinner:
I hope not, Algernon. It would put my table completely out. Your uncle would have to dine upstairs. Fortunately he is accustomed to that.
Wilde is holding up to ridicule the importance of having an even number at dinner parties. Lady Bracknell takes this so far that she is even willing to banish her husband upstairs so she can have the all-important even number at her dinner parties. The fact that he is "accustomed" to eating by himself suggests that this is not a one-off occurrence.
Apart from farce, this play also uses parody as part of its comic appeal, and this can be hilariously seen in the way that Cecily falls in love with Algernon before even meeting him. Wilde is clearly parodying the nature of love at first sight by taking it to this extreme level. Note what Cecily tells Jack about their engagement which happened a few weeks before they actually met:
Worn out by your entire ignorance of my existence, I determined to end the matter one way or the other, and after a long struggle with myself I accepted you under this dear old tree here.
For Cecily, never having met the object of her affections is no barrier at all to actually becoming engaged to him. Wilde clearly makes the concept of love at first sight preposterous by presenting it in this way, effectively parodying love and its impact on humans.