Normal practice (in a domestic garden, that is) is to prune the branches quite close to ground level. Dogwood twigs are produced on the stem in opposing pairs, so if you cut just above a pair of buds, two more branches will grow - like this:
So after a few seasons you can get lots of stems from each plant.
In retrospect I think I should have cut those branches shorter - maybe six inches or so above ground level.
In one corner of my garden I have adopted a different pruning strategy for a clump of Dogwoods. I have cut them at about 4 feet above ground level. They are therefore slim down below, with twiggy tops - almost like a "standard" shape:
|The green leaves belong to a Clematis plant which has become entangled with the Dogwoods|
I have kept the upward-pointing twigs, and removed most of the downward- or sideways-pointing ones.
What this means is that the plants growing at the base of these shrubs (currently Euphorbia and Primroses) get a decent amount of light, whilst I still get a host of brightly-coloured Dogwood stems.
|Euphorbia at the feet of the Dogwood plants|
Best practice suggests that you should prune your Dogwoods very severely in order to keep them vigorous, which in turn tends to produce stems with brighter colours. I usually trim mine quite gently each Spring to keep them from getting too big, and then give them a severe chop every 3 years or so. It seems to work for me.