Slice the onion so that the rings are relatively thick, then pick the ring that matches the size you want your fried eggs to be. Wider rings will create thinner fried eggs.
For thicker whites with a small surface area, use a smaller ring. Add oil to the pan, place the chosen onion ring in the oil, crack the egg into the ring, and let it cook.
For over-easy and over-hard eggs, you can leave the onion ring when flipping or wiggle it off right before. Onion rings can also be used for miniature frittatas and omelets.