With difficulty!

Depends if it growing along the ground or up a support eg tree or wall. If the latter cut it(or them) off at the base and leave it to die. When dead it can be pulled off fairly easily. Then if the stem at ground level is thick treat it with sbk stump killer.
If its growing along the ground just pull out as much as you can (haha) and then dig out the roots. This is hard work but it works. If you decide to take it to the tip don't leave it in the care overnight because it stinks and the smell lingers for days.

Some years ago, we cut down one which was growing up a wall. We sliced through at the base and left it to die (much easier to get off the wall when dead). We didn't treat the stump, and it never grew back.

Just thinking about NoseyPotter's ivy on his house though - just cutting the base didn't work for him, but it was a very large plant.

Thank you so much for this advice. What a wonderful site and members. x