Dig up small perennial weeds with a trowel, taking care to remove the entire root system and runners or shoots growing from the base of the plant.
Cut perennials off at their roots with a hoe. Remove all plant foliage, and then cover the ground with landscape fabric or black plastic. Weigh the material down with stones or bury the edges under soil to keep it in place on windy days. Leave the sheeting in place for one growing season and cut off any shoots that emerge from beneath it. Remove the sheeting in winter.
Crush or cut perennial foliage before spraying all plant parts with a ready-to-use systemic herbicide, such as 2 percent glyphosate, until thoroughly wet. Remove dead foliage after two or three weeks, after you see that the herbicide has taken effect.