This is a bit of a broad question, but I think if you are after the finest comedy in this excellent play, you need look no further than the interactions between Benedick and Beatrice and the kind of verbal dexterity that characterises their "merry war" as each makes clear the disdain that they feel for the other. Consider, for example, the following exchange from Act I scene 1. In response to Benedick stating that he "loves none," note how Beatrice responds:
A dear happiness to women. They would else have been troubled with a pernicious suitor. I thank God and my cold blood I am of your humour for that. I had rather hear my dog bark at a crow than a man swear he loves me.
To which Benedick responds that he would that God keeps her in this frame of mind so that some poor gentleman will escape "a predestinate scratched face." The wit and humour in such exchanges are by far the finest examples of comedy in the play, and are worthy of serious analysis. You might also like to look at the scenes containing Dogberry and how his stupidity and propensity to use malapropisms yields a different kind of comedy.