The oil needs to be slowly added to the egg, vinegar, and lemon juice base while being vigorously whisked. Only add more when the previous amount has been fully incorporated. I generally add the oil 1/4 cup at a time, dripping it very slowly into the base. Once the initial 1/4 cup has been added and emulsified it becomes a lot easier to incorporate the rest, and you can add it slightly faster, but still 1/4 cup at a time.
This is vastly simpler in a food processor. I have a Cuisinart 7-Cup Food Processor which has a little white pusher piece with a drip-hole in it. You can simply add the oil into this 1/4 cup at a time, it will slowly drip into the mix. Use the metal blade attachment.