When and how you prune your dogwood depends on what kind of dogwood you have.
If you have shrubby dogwoods they should be cut back fairly regularly to remove older stems and help prompt growth of new colorful stems. Other dogwoods require little or no pruning. Dead or deseased braches should be removed as soon as possible. Major pruning to reshape the dogwood should be done in late winter or early spring before growth begins. Take care not to cut into the back on the trunk as it can is thin and can be easily damaged. Bark damage can be an attraction for pests.