Step 5: Black magic.
The first bit to this is setting up. You need to make a little arch in your wick, like the photo.
Now try lighting it and pulling your thumb and forefinger across the chimney, the flame should disappear, now wave your hand past the lighter or blow on it.
If it doesn't relight then you need to adjust the shape of the wick, what you are looking to create is a little space underneath the arch in the wick where a small flame can effectively hide and stay lit when the larger flame is out.
The reason the lighter relights when you disturb it is that the flame catches the vapour coming from the top of the wick. Once you start to get a feel for this you can invent your own way of causing the lighter to re-light, I personally like setting it on a table and stealing the flame then snapping my fingers while swinging my hand over it.
Others include saying something and giving it a tiny shake or pretend to pop the essence of the flame in your mouth, then slowly bring your hand flat and level with the chimney. Blow gently across your hand and let onlookers be amazed.