When someone is caught lying. How now is self explainitory. Brown Cow means that they are a liar. Works incredibly well if they are exposed for their lie.
Guy 1: Hey, I know what the capital of Illinois is. It's Chicago.
"How now brown cow" is a phrase used in teaching a style of public speaking in which gesture, vocal production, and delivery are emphasized to demonstrate rounded vowel sounds.
Those four words roll off the tongue as a lighthearted way of asking "What's up? What's next?" And that tripping lightly stuff makes sense, since "How now, brown cow" has its origin in elocution, where the phrase was used to demonstrate properly rounded vowels.