For example, if I wanted to apply to CAS for NYU or Wharton for UPenn (not applying to either of those, but they’re well-known enough to use as examples), how would I do that?
Sign up for a free account on commonapp.org (available now) and do a search and enter the schools that you want to apply to and they will appear on your “dashboard” on the left hand side of the page, as will the supplemental questions/essays for each particular school.
In your example above, for UPenn, you would indicate “Wharton” on their supplemental question page when prompted to enter what college within Penn you would be applying to. Same for NYU or any other college that asks what school/college within the university you will be applying to.