To cut the onion, peel and then cut it so the root end is intact. Place the onion flat-side down on your board. Using the tip of your knife, make evenly spaced vertical cuts along the onion, just to the root end.
Holding onto the root end while lightly squeezing the onion to help hold its shape, carefully make two or three horizontal cuts just to the root.
Now you are ready to cut the onion into a uniform dice.
Why take the time to do it this way? For one, it's actually faster once you get the hang of it. Two, especially for this use, the relish will have a better mouth-feel if all of the vegetables are the same size. Three, you keep the onion fairly intact, preserving all its flavor rather than chopping it over and over again on your board.