Plants multiply by making seed, spreading their roots, adding rhizomes and multiplying bulbs. One way to tell if a lily or daffodil needs to be divided is that it has fewer flowers or seems to be healthy only around the outer edges of a clump.
Lilies are very good at making copies of themselves. Toward the end of the flowering season there are tiny lily seeds all along the stem and when the bulbs are dug up, there will be more bulbs under-ground than were originally planted. In addition, between the bulb in the ground and the surface of the soil, stem bulblets will be growing along the underground stem.
Now that lilies have bloomed and faded, we can dig up the bulbs and divide them to share or to re-plant. There are a few common methods you can use.
After digging, remove the roots of the bulb, being careful to not cut into the basal plate. The basal plate looks like the bottom of an onion and bulb scales are like layers of an onion.
Any bulbils and bulblets in the soil or attached to the plant stem can be planted directly into the ground or into planting trays and pots. They will probably take a year or two to build up enough size to bloom. They can also be collected and put into baggies in the refrigerator for a month before planting into pots and then kept protected over the winter.
Bulbs, bulbils, bulblets, and scales can be treated for fungus and disease before they are rooted or planted. Methods include spraying or dusting with fungicide, dusting with powdered sulphur or dipping in a one percent Clorox solution.
Lily scales can be separated from the main bulb. This method, called scaling or twin scaling, is very easy and popular among lily enthusiasts.
You can just dig down to the parent bulb, remove a pair of outer scales and put them into a baggie with damp Vermiculite until you see small bulblets have formed (2 to 12 weeks). Open the bag to keep the moisture at a minimum and the bulblets will continue to grow. Then plant them into trays or pots of soil.
Scales can also be pushed into a tray of half sand and half peat moss or seed starting mix, with the top sticking out. Moisten the tray bed and put it into a plastic bag or use a clear lid if the tray came with one. Keep them at 65 degrees until the bulblets form and then plant. Keep these tender plants inside until spring.
When digging daffodils that have stopped blooming, gardeners find offsets or small bulbs attached to the sides of the original central bulb. Offsets have a pointed growing tip and a root end and look like a miniature of the parent bulb.
To divide daffodil bulbs that do not bloom as much as they once did, dig them out of the ground and separate them. Separate each from the basal plate. They can be replanted as is or the large bulbs can be divided further.
To make more daffodil bulbs out of the ones you have, remove the outer skin and any stem from the top. Dunk the bulbs in Clorox solution or wipe with Clorox wipes. Then, with sharp knife that has been sterilized in bleach, cut the bulb into 4 quarters and dust with fungicide.
Put the pieces into slightly damp sand or perlite. Within a few months they will develop little bulbs. Plant the bulbs in pots or flats and then outside in spring. The same method works with hyacinth bulbs.