Use garden shears to cut away at thin vines. Place vine waste in a large trash can. Repeat until you have exposed the majority of the vine roots. You might need a hacksaw depending on the thickness of the vines.
Pull up the vine roots to prevent regrowth. If needed, use a garden shovel or spade to remove dirt to ensure all roots are uprooted.
Pull at vines to remove them from trees, house walls and fences. Use a ladder if needed to remove all vines from tree trunks and house walls to prevent regrowth. A ladder is also necessary when removing vines from trees so you can see what you are doing and therefore avoid pulling at a hornet's nest or other animal abode. It will also help you avoid pulling down dead tree branches, which can cause injuries.
Place all vine waste in a trash container or consider shredding it for use as compost.
Spread mulch over the ground where you have removed the vines to prevent regrowth. Try using wood chips, making the mulch bed about 6 inches deep.