You can prune dead branches at any time. If you’re pruning to renew the shape of a shrub, wait until after it flowers (if it’s a flowering shrub) and then prune it back. That will allow the plant to grow new branches and develop new flower buds over the summer months. When removing live branches, cut back to a bud that’s pointed in the direction you want the new growth to take. As a general caution, never remove more than one-third of a plant in any one year. If your shrubs are really overgrown, plan to reduce their size over 2 or 3 years.