There are proper and improper ways to try and remove poison ivy from an area. The main mistake people make is when they try to burn it out, because this puts the poison in the air where it can be breathed. More effective and less harmful ways to get rid of the poisonous plants involve a lot of labor.
Put on protective gear that will keep the poison on the leaves and in the stems from getting on your skin. Wear thick gloves, long pants and a long sleeve shirt, boots with thick socks, a bandanna around your neck and eye protection.
Pull as much of the ivy out with your gloved hands. Try to pull it out by the roots. You can also use a shovel if you have large clumps of the stuff. Put it in garbage bags as you go. You don't want to leave it lying around because you risk the chance that it could reroot.
Spray with an herbicide that will kill the plant down to the roots. Spray the entire area where the ivy was growing. This might take several applications. Mix the herbicide as strong as allowed according to the directions for best results.
Cover the area with dark plastic, boards, metal sheeting or anything else you can come up with. If the material is light, such as plastic, put rocks or something heavy down on the corners to keep it from blowing off. This cover will keep light off of the area, so the ivy can't regrow. Leave it on for at least a week to give the herbicide time to kill all the way down to the roots without the ivy growing.