Cut one 4-foot stake from 2-by-2-inch lumber for each post in your fence with a handsaw. Partially drive staples into one face of each stake with a staple gun, spacing them by about 3 or 4 inches. There should be staples from one end of the stake to its center, and they should be firmly embedded, but with enough space under the head to weave fishing line.
Screw each stake to a wooden fence post with 3-inch wood screws so that the half of the stake with the staples extends above the top of the fence. The staples should face to the side on which you want the cats to stay. If you have a chain-link fence, attach the stakes with loops of 18-gauge galvanized wire. Tighten the wire loops securely with pliers.
Unroll a roll of 36-inch plastic garden netting and use scissors to cut it into sections that are about 2 to 3 inches longer than the spacing between the posts.
Align one end of a section of netting with one of the stakes so that the bottom corner touches the top of the fence. Staple the bottom corner to the stake, then stretch the netting loosely along the stake and staple it to the top. There should be about 12 inches of netting extending beyond the top of the stake.
Stretch the netting loosely to an adjacent stake and staple it in the same way. The netting should hang loosely between the stakes and the top should fall to the side on which you want the cats to stay.
Weave the netting to the staples in the stakes with fishing line, then weave the fishing line through the sides and top edge of the overhanging portion of the netting. Staple the bottom of the netting to the top of the fence, if it's a wood fence. If it's chain link, weave the netting and the fencing together with fishing line.
Install the other sections of netting between the other stakes in the same way, then tie the sections together with fishing line.