To sign airplane, take your outstretched hand, and tuck in your middle and ring fingers. Then move your hand away from your body a short distance, as if flying, bobbing it back and forth a couple of times. If you move your hand a bit further up and out, slightly above your head, that's already the sign for fly.
Tucking in those two fingers is often difficult for an infant, and you will often see airplane simplified with either all four fingers tucked in, or with all fingers outstretched.
Airplane is a fun sign that we use in play. Use airplane when you see and hear a jet whooshing past, overhead. You can also use it in conjunction with an airplane toy, or a book that mentions a plane. Baby boys especially like this sign because it is so animated, and the sign resembles the motion of the actual thing.
Use airplane when you see and hear a jet whooshing past. When you sign airplane, think of your index or pointer finger as the nose of the plane, and your thumb and pinkie finger as the wings on either side.