Thanks for writing. Ivy can be a tough plant to get rid of, but it's not impossible. The easiest way is probably to spray the ivy with a product like Roundup. Once the plant starts to die, rip it up and watch for signs of regrowth. If there are sprouts that shoot up again, spray them or dig them out and continue this process until the ivy is no more.
Another option would be to pull and dig it out by hand. You can also try cutting it all to the ground level, then covering the area with plastic and mulch for a couple of years. That should exhaust the ivy's root system and you can pull the mulch and plastic away and resume planting.
---Justin, Senior Garden Editor, BHG.com