Are you talking about the Designs By Cuties area? I would love to know how to tell that as well.
For that matter I would love for there to be a search option within Designs by Cuties so that we can find a particular design (alphabet letter) without having to navigate to each page individually.
Lucy, the new design - will always be the closest to the left at the top of the page.
In every category - but not all categories have a new one everyday. It has been some time since for instance 'redwork' had a new one.