It’s a two step process - (1) be selected to interview with a sponsoring school and following the interview selected for interview with the Stamps Foundation, and (2) Stamps Foundation interview. The second seems like a formality though, as I’ve never heard of a case of the Stamps Foundation rejecting a student nominated by a sponsoring college. The Stamps Foundation interview seems more like a getting to know our scholars thing, and is very informal.
The Stamps scholarships differ across sponsoring schools and the first step different for each. At the most generous sponsoring schools, it’s an amazing opportunity. Good luck!