I just had to do this with my sister's reservation.

Open the reservation (can do this by searching for a reservation). I did this by opening my trips (go to myDelta, then click "open" in upcoming reservations. You should then have the option to use the trip finder at the top of the page)

Within the reservation, right under passenger name, you should see "add skymiles number"...or something to that effect.

After doing all of that yesterday...it wouldn't take it, and I had to call in anyway. What a joy