Spraying the poison ivy with a broadleaf herbicide can kill it and stop it from coming back. You need to exercise caution, however, since that broadleaf herbicide will also kill many other types of plants. But if you have a heavy infestation of poison ivy, spraying it thoroughly with a quality herbicide may be the best way to quickly eliminate the problem.
You can cover the poison ivy with a thick black plastic sheet or tarp and leave it in place until the vine is dead. Just be sure to weight the tarp or plastic down with rocks, bricks or other heavy items to keep it in place and stop the poison ivy from getting sunlight. Make sure to wear gloves to remove the poison ivy, even after you are certain it is dead. After removing the poison ivy you need to plant something else in its place right away. If you fail to do so the poison ivy will quickly reestablish itself.
Put on heavy gloves and dig a trench the whole way around the poison ivy plants. Dig down at least 6 to 8 inches to ensure you get below the roots. Dig out the roots under the poison ivy plants, making sure you get all the pieces of root. Pull the plants up from the top, touching them as little as possible. Place the plants in a heavy garbage bag for disposal, then check the soil again for any roots or root fragments. For this method to work, you need to eradicate the entire root system of the plant. Do not use this method if you are highly allergic to poison ivy. Even if you wear gloves, you could still get a lot of the poison ivy on you.
Pour a mixture of 1 gallon vinegar and 1 cup salt into a large pot. Place the pot on the stove over medium heat and stir until the salt dissolves. Allow the mixture to cool, then add 1 tbsp. dish washing liquid. Pour the solution into a spray bottle and aim it at the roots of the poison ivy plant. Be careful not to get the mixture on any other plants, since the salt can damage the root system. Spray the roots of the poison ivy thoroughly with the solution to kill the poison ivy down to the roots.