Early fall is the best time to plant shrubs in most regions, about six weeks before the first hard frost. The soil is still warm enough for roots to grow, the summer heat is gone, and fall rain does much of the watering for you. By the time next summer arrives, the shrub has a root system that can handle it.
Early spring is the close second, and the safer pick in cold climates (zone 4 and colder) or for shrubs that are borderline hardy in your area. Bare-root shrubs are the exception either way: plant those in late winter or early spring while they are still dormant. Avoid planting in mid-summer, when a new shrub spends all its energy surviving heat instead of rooting.
Whenever you plant, water deeply the first season. If you are still deciding what to plant where, OutdoorBrite can render shrub and bed ideas on a photo of your own yard before you dig.