Step 1: Slice
Cut the onions into slices about 1/4 inch thick — thin enough to ensure that they won't take forever to cook but not so thin that they'll become crisp.
Don't worry about crowding the skillet with too many slices; the onions will eventually cook down.
Step 2: Saute
Use about 2 tablespoons of olive oil for each large onion. Cook the onions over medium heat, stirring occasionally but not frequently.
During the next 15 minutes, they'll first soften and become translucent, then gradually turn slightly golden. But they're not caramelized yet.
Step 3: Wait
As the onions turn darker, stir more frequently (about once a minute) to prevent burning. When they're almost brown and have an intense, rich flavor, they're caramelized.
The exact amount of time required varies depending on the heat and the amount of onion in the skillet. Expect the process to take at least 25 minutes.