Once the call has connected, tap the star-shaped Effects icon.
Next, tap the Animoji button, then scroll horizontally and tap the Animoji you wish to use, and it will be displayed over your face.
Continue your call with your Animoji active, or tap the big None (X) button to deactivate it and return to the FaceTime menu.
Remember, tapping the smaller X above the Animoji menu means you can also apply other camera effects while on the call.
These FaceTime effects include filters, text, shapes and stickers.