That ivy may look good climbing up your walls, but it can get to be a nuisance. Ivy digs into walls, damages them, spreads quickly and smothers other nearby plants. Ivy plants are also quite hardy, which makes them notoriously hard to kill. If you want to kill an ivy plant, make sure the root is dead or it will come back with a vengeance.
Apply herbicide to new leaves when they start to bud in the spring and summer. Mature leaves build up a waxy coating that makes it difficult for herbicide to penetrate, but new leaves absorb herbicide easily, poisoning the ivy plant to the root. If you prefer, use bleach or white vinegar instead of herbicide.
Watch the ivy plant for two weeks for new leaves to appear. When they do, spray them with herbicide to kill the ivy.
Rake over the old leaves of the creeping ivy to cut them to allow herbicide to penetrate if new leaves cease to appear. Then, spray the old leaves with herbicide.
Pour boiling water on the base of the ivy if there are no other plants nearby that you wish to kill. Boiling water is a natural plant killer, and will help ensure that the root is really dead after the herbicide has done its work.
Dig up the ivy. You can wait until you have managed to kill the ivy, or start digging as soon as the plant starts to sicken. Don't worry about getting every last root out, as the herbicide and boiling water should have taken care of them.