Usually, when anime wants to make a character "ugly" for a gag (or just a character design) its mainly a matter of adding more details and lines. Drawing facial features that wouldn't normally be drawn (like nostrils and wrinkles), a lot of cross hatching on facial contours like cheek bones, and stark, dark shadows.
Source: Ouran High School Host Club
Source: Daily Lives of High School Boys
These two pictures are gags from anime with more normal styles, but if you want a more steady source of references for this kind of thing, I'd suggest looking at Cromartie High School and 80's action anime/manga like Fist of the North Star and the first few parts of Jojo's Bizarre Adventure (manga only).
Source: Cromartie High School
Source: Fist of the North Star
Most of the characters in the images above are guys, but the same principles work for female characters, too, as seen in the Cromartie High School example.
