The unorganic solution is to spray with glyphosate when it is actively growing. It may need more than one spraying, and be very careful not to get the mist on anything you want to keep.
The organic solution is to cut the ivy, let the leaves and shoots die off before removing carefully from whatever it is growing up. The roots will need to be dug up.
Beware that if it is growing up a wall it might have damaged the mortar which will likely need repointing once the ivy has gone, depends how long it has been there.
Whichever method, you might need to be as tenacious as it is
Nikki