I grow several different kinds of Clematis (but nowhere near as many as the fans on the Clematis forum!) and most of them like to scramble up through shrubs or trees, though C integrifolia prefers draping itself over the ground. Looks great with tuberous begonias in suitable colours and late-flowering daffodils

C integrifolia can be divided like a 'perennial' though it can take some time to settle back into growth.

C. tibetana showers seeds everywhere and, if they land in gravel, happily sprout to grow away.

C buchananii has stems like a ship's hawsers so the thought of layering or taking cuttings hasn't quite appealed. It's a real 'climb for the sky' sprawler but the bees love it in late autumn. On a fine day it literally hums with worker bees and bumbles.

Clematis such as 'Nelly Moser' have a suckering habit and these can be parted from the parent plant then grown on. Layering is also a possible. I'd use a mix of leaf mould and sharp grit to get a healthy root mass. It's said that the plant resents having its roots disturbed - and I'd agree, so I'd do any layering where I could lift the roots with a good wad of earth, nice and damp. About a month after severing the connection to the parent plant.

Patience is essential. I wish they were as obliging as strawberries but they aren't so I do my best to keep my busy fingers off for at least a year. Might be different in your area.

Good luck. They're lovely plants to have in the garden.