NO! You don't add more and more fat to your diet. Just start removing carbs. Don't ADD fat. Moderation is the key. Use butter, eat meat, just don't gorge.
You should read the Atkins book if you're really interested.
Gorging is what makes peple gain weight. As you say, moderation is the key. Move more, eat less. Doesn't matter very much what you eat, just eat less of it, and skip meals fairly frequently, say, 2 or 3 times a week.
Never eat when you're not hungry, and only eat when you are.