The trick to hand pulling weeds is to ensure you get all the root out as well, since many common weeds will resprout from roots, even fragments, especially those with tubers. This is often done most easily when the soil is wet, allowing weeds to be pulled more easily.
Gloves, knife, hand trowel, small pronged weeding fork or similar are useful.
Rake back ground mulch or organic material from base of the plant. Insert tool to loosen soil from around the roots. Grasp the stems or leaves of the plant at ground level and pull. Use the tool to free roots if necessary. Remove the plant and shake of any excess soil, taking care not to dislodge any root material.
Sometimes, only the growing heart of the plant needs to be removed not all the root material. If this is the case, use the knife to cut below the root system below the crown or underground stems and remove the plant while cutting lateral roots rather than levering the roots out.
Where the plant has a root system of underground rhizomes, tubers or similar organs from which new plants can reproduce, you must ensure all these are removed with the plant as well. After cutting out the plant, use the appropriate tool to clear the soil from around the immediate root zone of the first rhizome or tuber and trace the underground lateral stems / roots and remove any other rhizomes or tubers. Remove all the roots, rhizomes, tubers and any attached soil.
Minimizing soil disturbance is key to reducing germination of any weed seeds that might be present in the soil. Covering the area up with leaves, mulch or replanting desired plants helps cover disturbed areas.
Dispose of all weed material responsibly.
Keep in mind, weed seeds can often remain dormant for a long time. Ongoing maintenance of sites may be required for years after initial weeding, to ensure seedlings are removed before they can take hold and set seed themselves. Therefore plan your weeding accordingly.