Perhaps the simplest and fastest option is to erect a trellis -- or a series of trellises -- around the area you want to separate from the rest of the yard. A simple set of posts with wires stretched between them will get you started; around each trellis, plant fast-growing vines that will grow onto the wires. One option is trumpet creeper (Campsis radicans), which grows about 15 feet per year and is hardy from U.S. Department of Agriculture (USDA) plant hardiness zones 5 through 9. If you want an edible alternative, consider growing grapes (Vitis spp.), such as European grapes (Vitis viniferia), which are hardy in USDA zones 5 through 9 and grow 10 to 15 feet per year.
Hedges or bushes also can separate parts of the yard, though they will take longer to do the job you've enlisted them to do unless you buy ones that are already fairly large and well-established. An evergreen shrub is ideal for providing year-round yard separation because it won't lose its leaves in fall. A common choice is arborvitae (Thuja spp.), including the North American varieties, such as eastern arborvitae (Thuja occidentalis), hardy from USDA zones 2 through 7, and the fast-growing giant arborvitae (Thuja plicata), hardy from USDA zones 6 through 8a.
You already may have a fence surrounding your yard's perimeter, but you could install more fencing to divide areas within your yard. If you don't want to install a tall privacy fence, consider using a picket fence or split-rail fence, through which you'll be able to see more distant parts of your yard. Another option is to use a combination of several concepts and install a lattice fence, next to which you grow vines or other climbing plants.
Dividing your lawn doesn't have to involve a vertical structure or planting. Simply installing a path through an area can help divide spaces. Similarly, a patio can help separate one part of the yard from another part. If you decide to install a patio, then placing potted plants, planters or flowerbeds around it would block off the area a bit more from the surrounding space. Concrete, bricks, pavers or other materials can be used to make the patio.