If the area to be cleared is free from any desirable plants then use a glyphosate based weed killer. This will go down to the roots, several applications maybe necessary if regrowth appears. If the ground elder is amongst plants you want to keep, then hand fork as much of the elder root out as possible close to the plants. If practical lift the plants and get the elder out from the plant roots, disposing of those that are too infested or divide the clumps, saving the free ones. In between the plants then apply a weed killer carefully, or keep hoeing/forking the elder.
Hope this helps,