Remove all grass from under the chain-link fence and extending about 8 feet into your yard. Push a spade down into the grass just deep enough to penetrate through its root layer and into the soil below. Cut the grass in the area into several narrow strips, and roll them up to remove them. Pampas grass can grow 3 to 6 feet wide; making the planting bed 8 feet wide allows 1 to 2 1/2 feet of extra space at the front and rear of the planting bed so it has definition separate from the lawn.
Loosen the soil in the planting area to a depth of 8 to 12 inches, using a rototiller or garden hoe or other digging tools. If the native soil is poor and has slow drainage, remove up to one-half of the soil, and replace it with finished compost, manure and other organic materials. Blend those soil amendments thoroughly with the native soil.
Spread the amended soil evenly, using the back of a bow rake to drag the soil into place.
Stretch a garden hose in the planting bed so the hose runs parallel with the chain-link fence and rests halfway between the fence and the front edge of the planting bed. Measure along the hose, and push temporary stakes in the ground every 3 or 4 feet, depending on the mature width of your pampas grass variety. Remove the hose. The stakes mark the planting locations for the pampas grass plants. Although the grass can grow up to 6 feet wide, the close spacing ensures that the plants fill the area and hide the chain-link fence quickly.
Select one stake you pushed into the ground, remove it and dig a planting hole in that location. Make the hole twice the diameter of one pampas grass plant's root ball and the same depth as the plant's nursery container. Dig a planting hole at each stake's location, matching each hole's depth and width to the hole's designated pampas grass plant.
Set each pampas grass plant in its planting hole so the top of the plant's root ball rests even with the surrounding soil. Fill the remainder of each planting hole with the soil you removed to create the holes. Pack the soil gently, removing air pockets. Adjust plants and soil as needed to make the plants stand upright.
Spread a 3-inch layer of organic mulch, such as fine, bark chip mulch, around the plants to cover the bare soil. Do not push the mulch directly against the plants' bases. Spread a 4-inch or deeper layer of mulch directly beneath the chain-link fence. Mulch helps to prevent grass and weeds from growing. Using mulch really makes the difference between the pampas grass looking like an intentional planting and simply unkempt grass.
Water the entire planting bed well, until the soil and pampas grass' root balls are evenly moist. Water the plants deeply about once weekly until they become established in the soil and show new growth. After establishment, pampas grass needs watering only during periods of drought.
Apply an all-purpose, water-soluble fertilizer, such as 10-10-10, to the pampas grass plants about once monthly during spring and summer. Mix 1 tablespoon of the fertilizer with 1 gallon of water to prepare the fertilizer for use on the pampas grass.
Place field stones, bricks, paving stones or landscape timbers along the sides of the pampas grass planting bed. The edging further defines the planting bed and separates it from lawn.
Allow a few months for the pampas grass to fill in and completely hide the chain-link fence. The rate of growth varies among pampas grass cultivars. For example, Sun Stripe variegated pampas grass (Cortaderia selloana "Monvin") grows fast while "Gold Band" pampas grass (Cortaderia selloana "Gold Band") is slower to fill a space. Both cultivars are hardy in USDA zones 7 through 11.
Leave dried flower plumes on the pampas grass plants over winter if you want them to add color and texture to the garden. If you prefer to cut back the plumes, the pampas grass probably still will be tall enough to hide the chain-link fence; typically, a chain-link fence near a house is 4 feet tall. Even Ivory Feathers dwarf pampas grass (Cortaderia selloana "Pumila") grows 3 to 5 feet tall. That cultivar is hardy in USDA zones 7 through 11.