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Try freezing onions for 20 minutes before chopping them, to stop your eyes from watering. Once cut, an onion should be wrapped, refrigerated and used within 4 days.
Cut the onion in half, slicing downwards through the root, then peel.
Cut 5-6 vertical slices into each half, leaving the root intact.
Lay the onion half flat, slicing horizontally and keeping the root intact.
Slice downwards across these cuts to dice.