Spray with Roundup or dig or both. Depends what the weeds are really.

Nettles are relatively easy compared to things like docks and dandelions, not to mention horsetail or Japanese knotweed! With gloves, unless like me you're a bit of a masochist, pull the nettles out and a good tug usually removes a lot of the underground stems as well. They tend to root along the surface. Keep doing this and they will soon disappear.
With docks, there is no alternative to digging them out with a spade, and even then it's likely any broken bit of root will grow again. A good dab of Roundup on the leaves will do a more permanent job if you don't mind using weedkiller.