The brake band is attached to the internal brake tensioner using a Lark's Head knot. To remove the old brake band, first disconnect the spring from the eye:
Next, slacken the brake tensioner by turning the wooden brake adjustment knob counterclockwise while you pull on the swivel of the brake band: 
Use a needle or the pick from your miniSpinner Maintenance Kit to open the Lark's Head knot on the swivel:
Open up the loop and pull the spring and the rest of the brake band through the loop:
Slid off the swivel:
To install the new brake band, thread the loop from the brake tensioner through the eye of the swivel:
Then, thread the spring and the rest of the brake band through the loop:
Pull it tight...
Then reconnect the spring and you're done:
