Fill spray bottle with vinegar
Spray weeds thoroughly with vinegar, taking care not to spray grass or other plants. It'll kill them too!
Let sit for a day or so.
Spray again if needed. You want the weeds to be pretty thoroughly brown before trying to remove them.
Gently try to pull weeds out after a rain. Grasp the weeds by the base and gently wiggle and pull 'til they release from the soil.