Sure it's true that we may want to divide plants before they get out of hand, as well. It's a great way to repeat color in our landscape. It's also smart to fill in dead spots with something you know grows well in your garden. Some people I know just don't learn. They keep replacing that plant that died with the same thing in the same place. Sometimes we just can't have that plant there no matter how much we'd love it. Maybe it can't tolerate those conditions or the foot traffic or your pets or other pesky animals that are definitely not pets. Why not divide a plant whose habits and needs you know very well.
Plants that spread readily by sending out new roots are the best candidates for dividing. There are many ways to divide plants and many plants whose root structure lends itself to dividing much more than others. Dividing a plant means that you will be doing a combination of cutting into roots and separating or untangling the roots. This can be done while the plant remains in the soil or once the entire plant is removed from the soil. Each method has it's advantages. Cutting through the roots with a spade can be done while the plant is still in the ground. The rest of the plant remains undisturbed. Digging the entire plant out of the ground is done when you don't want to cause undue damage to the roots and you want to be more precise with the separating of crowns and roots. This is often done with hostas because once you can get a good look at the roots it is usually clear where you'll want to cut. Cutting can be done with a kitchen knife for precision. I like to use a serrated knife.
I keep one handy on my potting bench.
There are plants that do not multiply but instead come back strong every year. They may have a main tap root that goes deep into the soil cannot be divided but often leaf or root cuttings can be taken to multiply these gems in your garden. These are often the plants that multiply by seed as well. Leave the soil around them loose and clear of too much mulch that would prevent the seeds from contact with the soil they need. But that's a whole different kind of math than what were concerned with here.
Once you've divided your plants get them in the ground right away or at least keep them moist. Don't wait too long to get them in the garden. Give them the best chance to establish new roots before the first frost hits.
I can't wait to get right at this but tonight I'll have to be satisfied with listing the plants that need dividing and listening to the owls in the woods. Huhuhuhuh hoo hoo hoo