While I don't mind the scratches and scrapes I get working in our yard, I don't like the itchy rash I get from poison ivy.
Poison ivy is a tall vine that climbs dead or living trees and shrubs. The chemical that causes the rash, urushiol, is present in all parts of poison ivy plant. Even in winter if you damage a stem or root, you can get a rash. Some people are severely allergic to urushiol, so shouldn't work around the plant.
Although poison ivy is a vigorous grower and likes the edge of forests, partly sunny areas and even can creep on the ground. It's a native plant and not considered invasive. In fact, poison ivy has some good attributes. Many insects and animals feed on the leaves, the tall vines create a wind buffer at the edge of a forest, and the white berries are a bird food source. So, if you have poison ivy on your property that's not causing harm, leave it.
First identify the vine. The stems have hairy, aerial roots that attach to trees. The plant has 3 leaflet leaves with jagged edges. The young leaves can be red, while older leaves are green. If you must remove it, be diligent. Poison ivy will regrow from roots left in the ground. If mowed down continually, it will adapt by growing as a creeper with smaller leaves. And never burn poison ivy.
Wear protective clothes, gloves and boots, and dig out the root system. For thick vines, repeatedly paint a specific herbicide on the cut stump. Wash clothes and yourself well after working.