Activating Deep Abdominal Muscles: Flat Belly

After my Ballet Sculpt class yesterday, a participant (the Lovely Ms Lydia) admitted she struggled with the abdominal exercises that required raising the feet off the ground. Her lower back arched and she felt a strain. This is common when you're not relying on your deep abdominal muscles to stabilise (transverse abdominus or TA). TA is like a corset of muscle that encircles the spine - ensuring alignment from the ribs to the hips.
How do you know if you're using TA and how can you strengthen it?

Here are three methods - maybe one works for you, maybe all three!

Lie on your back with knees bent and feet on the ground hip distance apart.
Slightly tilt your pelvis up towards your ribs and sink your belly button towards your spine.
Release.
Repeat.

Standing tall, feet hip distance apart.
Imagine you're trying to zip up your skinny jeans.
Draw your navel in and imagine lifting it towards your ribcage.

This last one is barre3 founder Sadie Lincoln's advice:
Place your own hand on the low belly. 
Without gripping or pushing the abs out, sink your navel back. 
Your hand will follow like it is sinking in wet sand. 
Once you have accomplished this think of the navel scooping in and up towards your sternum.