With a garden spade dig up the plant with the largest root ball you can manage
Wash off some of the dirt from the plant roots so you can see where to separate the roots, in between major stems, for example. Sometimes there will be visible plantlets that can be separated.
If the root ball is soft enough you can separate it with your hands or a garden fork. But for tougher plants (such as asters) you will need a cutting tool like a garden knife to separate the plant.
Be careful not to divide the plant into too many sections, the sections should all have a good amount of root mass. Be sure not to divide a plant more frequently than once every 3 years.