The airplane carrying position is great for when you are just playing with the baby and still want to work her back and neck muscles.
How you do it is you place you arms underneath your baby from the front and back so she is lying on her stomach and then just hold her in front of you like below.
It's important to keep it fun when engaging the baby in an exercise that's hard on her body. To keep Emily from fussing, I sing songs and make funny noises; the sillier the better!