There are hundreds of varieties of ornamental shrubs, each with its own care requirements. But to determine proper care--how much to water, when to fertilize, how much, and when, to prune--the first order of business is to determine what type of shrub it is. Identifying an ornamental shrub can be challenging, but there are plenty of resources to help.
Narrow down options by determining whether the shrub is evergreen or deciduous. Evergreen shrubs retain their color, and their leaves, year-round, and generally have needle-like leaves that retain water. Deciduous shrubs tend to have flat, broad leaves and lose their leaves every autumn. Evergreen shrubs rarely flower, while deciduous shrubs often have dazzling blooms, almost always in the springtime.
Clip a stem off the plant with several leaves, and take a digital photo of the entire plant.
Scour the Internet for online identification guides (see Resources). Both the Deciduous Shrubs Identification guide, with 55 pages of photos, and Louisiana State University's Evergreen Shrubs Database, a lengthy list of more than 70 specimens with links that lead to photos and detailed descriptions, should prove valuable.
Hit the books. Visit the nearest library or bookstore, leaves and digital photo in hand, and browse through such authoritative reference books as Ornamental Plants: Their Care, Use, Propagation, & Identification by D. Dwight Wait (1994, Addendum); the Sunset Western Garden Book (Sunset Books, 2001); and the Back Pocket Guide to Ornamental Plants by E. Wesley Conner (VEP, no date listed). Compare specimens and photos of the shrub in question with the photos in the books.
Visit the nearest nursery, again with leaf sample and digital photo in hand, and ask to speak to a plant expert. Most nurseries tend to employ people well-versed not just in what plants the nursery carries but also with the broader range of plants that can grow in that region.