Besides saving money, there are three other reasons to divide plants: to maintain good health, beauty and size. Overcrowded plants will become stressed. The soil can become depleted of nutrients, and fungi and pests could invade without proper air circulation. Overcrowded plants also produce smaller flowers and leaves. You might see faded flowers and foliage because they can't take up enough nutrients from the soil. Additionally, there is only so much space in your yard. Some excessive growers including yarrow and artemisia will need to be divided every year or two to maintain size.
Spring and fall are good times to divide. You should do it when it isn't too hot or too cold, but don't divide during that plant's blooming season. Early spring works well when planning to plant the divisions because it gives the new plants time to become established. Some plants to divide in spring are yarrow, aster and garden mums. Fall works well for dividing to improve the health and control the spread of plants. In the fall, irises, black-eyed susans, ornamental grasses and summer-blooming bulbs are typically divided.
The process is different for dividing different types of plants. Some bulbs, like daffodils and dahlias, will produce "bulblets" or "fat fingers," which are new bulbs grown from the original. To divide these, make a clean cut to separate the baby from the original bulb. Then replant this like any other bulb. Other plants you'll divide are perennials, grasses and lily-type plants like agapanthus, which will all either benefit from division or can easily be divided to create more plants. Plants that can't be divided are those with single rootstocks like trees, shrubs and vines.
To divide perennials, start by watering the plant thoroughly two days in advance. Either remove the plant from its pot or dig the soil away from the roots in the ground. Look for a spot where an offshoot can be separated. If dividing for health reasons only, identify the problem areas you need to remove. Use a sharp knife, scissors, garden pruners or a special plant-dividing knife with a serrated blade. Whatever you choose, you can disinfect it easily with anti-bacterial hand wipes.
Use the tip of the blade to pry off an offshoot at a natural dividing point on the plant's base. Once you make the separation, pull apart the sections. If you have a plant with a thick root system like a grass, simply cut out a chunk of the roots. Plant these new divisions just like you planted the original, giving them plenty of water in the beginning to help them get established. If you divided to remove damaged areas, throw away the sections you removed.