With extreme difficulty !!!! A continual spray of double strength Glyphosate based herbicide may do it....but it could take a year or two to kill it all off.

This question has been asked many times on here, including one a few days ago. If you type Ground Elder into the search box at the top of the page on the right you can read all the replies over the years.

What it amounts to is constant vigilance, dig out what you can see and all the roots you can find and keep doing it without letup. Or you can use glyphosate which will gradually weaken it - do it every time it appears again. Or a combination of these.