Rip out or use a weed whacker to remove the ground ivy from your lawn. Try to remove all of the roots and pieces of the ground ivy so that it doesn't grow back.
Spray a weed killer like Weed Be Gone, which is specifically meant to kill creeping Charlie. Ground ivy can be difficult to kill, but weed killers are the best management. You might have to apply the spray in the spring and fall as well as a few times in between depending on how persistent your ivy is.
Monitor your lawn and watch for any new sprouts of ground ivy. If you see any, pull them out and spray more weed killer.
Till the soil during the spring and plant some grass seeds after the ivy is completely gone. Put hay over top of the grass seeds to prevent them from blowing away or being swept away by the rain. Planting grass can help blend in the rest of your lawn with the area where the ground ivy was.