That Zoolander quote is an incredibly appropriate way to describe the Fashion Battles in That's QT. About every other month in game time, the anthropomorphic mailbox character will pop up and deliver a challenge to the player from one of the designers. You can either accept or decline (the first option is accept), and after that you are whisked to the event hall.
The contest arena looks like the set of some cheesy game show. The three judges are seated in garish mini-cars, and an announcer with a huge bow-tie introduces your opponent and you to the audience.
After you've accepted the irony that an announcer of a fashion showdown would wear such clothes, five cards appear on the screen, each showing certain clothing items on a model. One of them is randomly chosen, and then you are given the opportunity to dress your model.
I've found the best thing to do is go with what sells. When you touch an article of clothing on the bottom screen, the top screen will display it and also show how many people have purchased it from your shop. Pick items from the highlighted clothing tabs and add them to your model, then click the lower left button.
You're probably wonder, "But what if nothing's selling?" In that case, look at the audience. See if any of them are wearing items you created. If so, have your model wear that.
You will then receive a series of scores. You'll be given a general score, an audience score, scores from the judges and then another series of scores for some random reason. (So many scores flash past, I wouldn't be surprised if one of them is a "showing up" score.)
At the end, the winner will be heralded and given a prize. It is incredibly easy to win if you just go with your best selling pieces, so don't get stressed about it and have fun. I've noticed that, after winning, your shop gets a brief popularity surge as well, so it pays to always look your best.
Images courtesy of Koei.