DL operates out of Terminal 1, Boarding Area C (C gates). AS operates out of the International Terminal, Boarding Area A (A gates). There is no airside connection that I'm aware of between them, you'll need to exit security and reclear.

I would just walk between terminals. Turn right when you exit security and go down the escalators. You'll eventually pass some exhibits from the flight museum and a bunch of check-in counters. The C checkpoint is past the Delta checkin counters. You can also take the AirTrain, but it won't save you much time or that much walking.

T1-C and T2 are now connected airside. T2 has better food options.