For looking after tubers, have a look at :-
http://www.allotments4all.co.uk/joomla/component/option,com_smf/Itemid,91/topic,28501.0http://www.allotments4all.co.uk/joomla/component/option,com_smf/Itemid,91/topic,28522.0As for propagation from tubers/dividing a clump :-
Large tuber clumps can be divided either in the autumn or the spring. When dividing, each piece needs to have an eye. The eyes are located near the old stem of the clump. Eyes are easier to locate in the spring, but large clumps take up more over wintering space and are more likely to rot. All cuts should be dusted with yellow sulphur to prevent rotting.
The best flowers come from one or two year old tubers. Exhibitors use basal cuttings and chuck the tuber.
I would certainly recommend dividing up a 20" clump. The best bits will be around the edge. The middle is probably just pith and dead tuber, as this was the original plant.
I try not to cut tubers, but use my hands and brute force as this means they break at the natural weekest point. However I usually have a bread knife handy.
As for looking after them ... the following is part of a Fact Sheet I wrote for a local garden centre ... Are you sitting comfortably ?
7. Cultivation
Planting
Most Dahlias are planted as tubers from late spring to early summer, once all chance of frost has gone. The exact time depends on when the plant is needed to flower; it takes between 70 and 140 days from planting to flowering, depending on variety. For exhibitors, the timing of planting to co-ordinate with show schedules is a fine art. For the gardener, spreading the planting over a period of several weeks will lengthen the flowering period.
Tubers should be planted about 10cm (3-4 inches) deep, and 30-60cm (12-24 inches) apart, depending on expected size. If dahlias are planted too close together, they will compete for sun and water, resulting in disappointing flowers.
Seeds can also be sown, from February onwards. Germination is straight forward, a propagator on a sunny windowsill is adequate. Young plants should be hardened-off and planted out in early summer.
Care during the growing period
Once growth is under way, a handful of a balanced fertiliser and a good watering is all the dahlia needs for strong growth.
As the dahlia is a tall herbaceous plant, it has trouble supporting itself, especially in wind; thus it is always advisable to stake plants.
As mentioned above, the dahlia is a thirsty plant and needs 25mm (1 inch) of water a week. This should be applied as directly to the roots as possible. Watering the leaves in hot weather just causes scorching.
Stopping, Flowering and Feeding
Once the plant has grown to the required height, it should be ‘stopped’, ie the growing tip should be removed. This will reduce the natural apical dominance and encourage the plant to produce side shoots from the buds in the leaf axils. More shoots means more flowers. The exhibitor can also use this to control the flowering times. A flower head that is less than 20cm (8inches) across (ie a ‘medium’ classification or less), it takes 8 weeks from stopping to flowering, longer for larger blooms. At this stage, a high potash feed should be applied.
As the plant starts to produce flower buds, the exhibitor will remove all wing buds (side buds), just leaving the main crown bud. At the same time the lower third of leaves should be removed. This reduces overall water usage and allows the shoot to concentrate on a single, and much larger, flower head.
The gardener may wish to leave all wing buds on to increase the number of flower heads, but they will be reduced in size.
Dead heading
As the season progresses, flower heads will come and go. Removing the old ones has the same effect disbudding, in that it reduces apical dominance Hence more shoots will be produced and therefore more flower heads
This will continue right into November, when the day length shortens to less than 10 hours and sun strength and temperatures drop.
Lifting and Storing Tubers
Lifting tubers should be done about 2 weeks after a killing frost, the plants will turn brown if frosted hard enough. Tubers dug too early are still "green" and will not store. Cut the stalk off to about 6", gently lift tubers with a spade or fork carefully so as not to break the necks. Wash dirt from the roots and allow to air dry. Tubers with large stems should be hung upside down to prevent water collecting at the plant base, and rotting the tuber.
Once dry, tubers should be trimmed, any root less than the thickness of a pencil should be removed.
Tubers should be stored in crates or cardboard boxes. Containers lined with 10-12 sheets of newspaper are best. Never store in sealed plastic bags or plastic containers. Tubers should be packed in a storage medium such as slightly dampened peat, sand, or straw.
Store in a cool, dry area (temp. of 40-50 F, 70% humidity). Too warm they will wrinkle/shrivel and too cold they will freeze/rot. Tubers should be checked once a month throughout the winter months.
Hope that helps.