how do I take cuttings of shrubs

Hazel trees produce suckers around the base of the tree themselves. Carefully dig these up with plenty of root and pot them on before planting out. Honeysuckles should work from green non-flowering cuttings (spring and summer, but keep them shaded and moist, and pot into vermiculite or similar) or ripe or semi ripe cuttings in the autumn for winter in sandy soil.
I haven't tried Berberis but from what I have read any small leafy cuttings should root easily if put into a sandy (or vermiculite) mixture with some gentle bottom heat, and kept moist, but not wet.