The main reason for growing dogwoods in your garden is that they provide great winter interest with their colourful red, purple and yellow stems.  To achieve this effect, they should be pruned in early spring.  First of all take out all dead and diseased wood and any small and spindly growth.  Then prune all the remaining healthy branches back to the first pair of healthy buds nearest to the base and then take out any crossing or twisting stems.  The aim is to achieve a simple open structure to encourage colourful new stems to emerge the following winter.