The methods of propagation match those for reproduction outlined on the genus page.
If a plant has been identified as having offsets, ( see reproduction from rhizomes), the tuber should be dug up after it's gone dormant and the offset removed with a sharp knife. The cut surfaces should be treated with 'Flowers of Sulphur' or a similar powder fungicide.The offsets are then planted like any other tuber, (see Cultivation).
When a stoloniferous plant has formed a clump, it can be divided when it's gone dormant and the sections replanted. Don't be too greedy: I once destroyed a Campanula by cutting it up into too any small pieces!
Fertilized flowers develop into green berries which slowly turn red as they ripen. This is another problem we have at Redhall: species which flower early in the year can set fruit which will ripen by October and can then have the seed extracted for planting. However, the later flowering species don't get past the green stage before the stem collapses as the plant goes dormant. We are experimenting to counter this by cutting off the stems before they collapse and keeping them in water in the conservatory. This allows the berries to ripen but we've yet to see if the seed is fertile.
As with other genera, when germininating seeds, I try to mimic what happens in nature. The seeds are sown in autumn when the plants go dormant. The red berries are squashed under running water in a stainless steel sieve with the back of a wooden spoon until all the flesh has been removed. They are then planted in a deep seed tray with a thin layer of compost on top and left until spring. It's important to wear latex gloves whilst doing this as the fruit contains a skin irritant. 
In their first year, some species will only grow a tuber without any leaves. I keep a tray of seeds for at least two years; potting them up when the tuber is large enought to handle.