How do you lose fat?

In a nutshell, it's a simple law of energy intake and expenditure. Eating more than you are using means you gain weight. Burning more than your eating means you lose weight... Unfortunately the real outworking of this is not so simple. Losing fat (for most people) is hard -- get used to the idea then you won't struggle so much with disappointment.
There are 5 principles to keep in mind - Diet (Nutrition), Cardio (Exercise), Dedication (Consistency), Goals, Weight training. It is possible to lose fat with correct diet alone (for some people) - but the best chance of success will be to apply all these principles. Even the perfect diet plan can fail if you cannot stick to it.