First, remove some, but not all, of the end. Make sure to leave a little of the root intact, as this will make the next steps easier. Peel the onion and discard the peel.
Stand your onion on one of the now-flat ends. Chop in half with your chef's knife.
Lay a single half on the flat end. Working from root to cut end, make several cuts at dice width that cut almost to the root end, but leave a little bit still attached.
Working perpendicular to your last set of cuts, make another set of cuts at dice width. This will leave you with cut pieces. When you get to the portion with the root, discard it.
Repeat for your other onion half.
During cooking, the layers should flake apart leaving dice sized pieces.