Dividing clumping plants is one of the easiest ways to propogate and get free plants to fill gaps around the garden. I have used Black Mondo grass here, but the principals apply to many other plants.
Black Mondo's are a very easy plant to divided and use to fill spaces through the garden. Before starting give it a good water to decrease the shock to the roots.
Soak clumps in a bucket with 20mm Seasol. This also aids with plants recovery and gives them a good boost. It also help loosen soil around the roots.
Pull the plants apart, you will need to be a bit vigorous to seperate out the individual clumps.