Welcome to ATP.
'When' - Spring in New Zealand (September/October?) is what they advise on New Zealand gardening sites. The Chrysanthemum plants benefit from a good 'haircut' or 'trimming' in the Spring to encourage a more bushy growth habit and more blooms; when you cut back the spring growth you can hopefully grow a new plant from each piece cut from the mother plant.
As for 'how' I usually use a cutting about 6" - 8" long, removing the lower leaves and remove the growing tip, dip into rooting hormone gel and place into damp vermiculite. Pretty good success rate using that method.
