Install a physical barrier around the planting area. Use sheet aluminum or galvanized steel. Bury it so it extends at least 12 to 18 inches down from the surface of the soil to block the roots from traveling outside of the growing bed.
Remove any vines that grow onto trees promptly. Cut the vine off near ground level. In a few days, the top growth will die back and can be easily pulled down. Dig out as much of the roots as possible. Monitor the spot and hand-pull any new plants that start growing from stray pieces of root that you missed when digging them out.
Apply non-selective, systemic herbicide, such as 2,4-D, to control ivy growth in lawn areas or other areas. Because the leaves are waxy, dab the herbicide directly onto the leaves with a cotton swab.
Remove faded flowers and any berries that form, as they contain seeds. The birds eat the berries and spread the seeds all over your property.