Wow, they put a lot of thought into this:

What does it mean to cry ugly? Beyoncé, beautiful talent phenomenon, does not know. At her concert last night, she teared up like a sad angel and said: "I'm giving y'all the ugly cry." Alas, she was not. Though she has made one notable previous attempt (citation 1: "Why Don't You Love Me"), she has not mastered central elements of this facial activity. As a primer, for all of us, here is the anatomy of the Ugly Cry.

You might think that Ugly Crying is in the eyes, which produce the necessary fluid, but it's not. Ugly Crying is 60 percent lips. This is demonstrated exceptionally by Ugly Crying's reigning expert, Claire Danes, and by Ugly Crying OG Diane Keaton

The lips somehow both collapse upon themselves and expand in breadth. 

When Harry Met Sally! What a great movie!!

( http://mashable.com/2013/07/22/sad-gifs/ )

Well now I know what "cry me a river" looks like.