I did not apply through my college - instead just applied through AmEx's online system.
Started off with two back-to-back phone interviews. Questions were entirely behavioral in nature and started off with the typical "tell me about yourself/walk me through your resume". AmEx employees generally kick of the interview off by telling you all about themselves - taking away the chance for you to ask it yourself when the interview winds down and they ask you if you have any questions.
Round 2 for a summer internship involved going down to the Manhattan office for 2 face-to-face interviews. The time in between those interviews is filled with awkward conversation with recent MBA hires who tell you over and over again "how cool it is to work here" and how enjoyable the "blue space" concept is. There was also a lunch where a random Executive VP talked for 10 minutes about how awesome he was.
I really got the impression that AmEx Operations, and especially the Global Services division, is full of socially awkward people. Most of their employees have engineering backgrounds...and it shows.