Setting aside the issue of JFK, I have found that the vestigial stand-by policy is one of the least well understood of DL's elite benefits---including by their own agents. IME, by far the best way to go about this is to list yourself through the kiosks. Once you're on the lists, I've found the GAs are competent at managing it, but I frequently encounter ignorance (feigned or not, I cannot tell) from agents about how to put someone on it.

To answer a previous poster, it is my understanding that you can only be added to the standby list at the airport; phone agents cannot help you as it is not part of the reservation system to my understanding.