Pull up the shallow rooted ivy when the ground is wet. Spray with ivy killer but you will find deep rooted ivy slow to go and difficult to polish off completely.

If it's mature and growing up a fence/ tree/ wall and you want to get rid of it, you need to saw through the trunk near the ground. Then you wait for the top growth to die, or you can speed things up if you want by pulling off as much as you can reach.
If it's sprawling over the ground, just haul it out, and keep hauling.