Wear heavy gloves and long sleeves to protect skin. Nettles will cause a rash on your skin.
Dig deep around the plant with a trowel or other digging tool. Be sure to remove all of the root.
Hoe repeatedly to destroy the roots. When hoeing, raise the hoe over the root and bring the sharp end down over the root to cut it. Pull the hoe towards you to rip any remaining roots out of the ground before lifting and repeating the process. The hoeing process entails severing the root and dragging it out of the ground.
Compost any un-flowered tops but burn or bag the roots.
Apply weedkiller to emerging shoots in spring and any re-emerging sprouts following mechanical removal.