Because privet hedges grow so enthusiastically, and aren't susceptible to disease, they make great privacy borders. They fill in quickly and keep an area filled. In fact, one of the few things you need to do is just make sure they don't grow out of their bounds.
Prune privet hedges in spring and fall. You won't get a formal, clipped hedge look with privet hedge, but you can keep them in a neat, well-rounded shape by going out in early spring and again in late fall with a sturdy pair of hedge clippers. Trim off any branches that look dead, diseased or weak, then trim for shape. Cut back overly long branches and trim off lateral branches where the hedge looks too crowded and messy.
Watch for invasiveness. As privet hedges maintain healthy growth, you'll see lots of new shoots around the base of each shrub, which can (and will) develop into large shrubs themselves if given the chance. Remove young shoots, unless you want to fill in an empty space.
Space out nearby plantings. Try not to plant anything very close to a privet hedge, both to give the hedge room to grow and breathe and to protect nearby plantings from being overtaken by the privet. You also need room to get in there and prune as needed, so don't crowd out your room with tender flowers or small shrubs that will be injured. An exception would be a sturdy groundcover, which can grow near and even under the privet and endure some tramping without adverse effects.