Mow over ivy wherever it grows on the ground. Standard push mowers and riding mowers are generally tough enough to mow over ivy.
Remove roots and stems by physically pulling them from the ground. This is easiest when the ground is soft after a rain. Minimize root breakage, because roots left in the ground can sprout and regrow. Use a shovel or spade to dig up roots that cannot be pulled out.
Remove ivy from trees by cutting off the vines a few inches above the ground with a strong set of pruning shears. Wait for the vines to turn brown and die, then peel them off the trees. Use a ladder to reach high vines if necessary. The ivy roots can be pulled out or dug up, but be careful not to injure your trees' roots.
Look for a herbicide that contains glyphosate. Glyphosate is a widely used chemical in herbicides, and it is one of the most effective and relatively safe for removing ivy.
Spray ivy with glyphosate in early spring as new growth emerges. Focus on green leaves and spray until wet. Spraying later in the season is less effective, because ivy leaves develop a protective waxy coating as they mature.
Avoid spraying glyphosate on desirable plants; it is a powerful herbicide capable of killing a wide spectrum of plant life. Also avoid getting it on your shoes and clothing, and carefully follow all instructions on the bottle.