Chopping an onion efficiently is one of the most fundamental knife skills in any kitchen. Start by cutting the onion in half from root to tip, then peel away the outer layers.
Place the flat side down on your cutting board. Make horizontal cuts parallel to the board without cutting through the root end — the root holds everything together. Then make vertical cuts from tip toward the root, and finally slice across to create a fine dice.
To reduce tears, keep your onion cold before cutting, and use a very sharp knife. A sharp blade releases fewer of the irritating compounds that cause your eyes to water.