The simple method: EAT NOTHING BUT UNPROCESSED FOOD!
In other words , only food that your great, great, great grandmother would recognise on a plate. Eating solely in this way would be my preferred option as it's without doubt the healthiest way of losing fat even though it'll take a little longer than the other methods below. When you eat nothing but 'clean' food , your body will change to it's ideal state. You may not get a perfect 6 pack but you'll get lean and are very unlikely to lose muscle mass.
Some common foods that are NOT unprocessed:
Bread, pasta, rice, cheese, (most) milk, flour, soy products.
Unprocessed food: any meats, any vegetables, olive oil, legumes, beans, oats, potatoes, dairy products like eggs, fruit.
This method is also referred to as Paleolithic diet.
High protein diet:
This isn't so much a fad diet but a pretty sensible way of eating :
Consume one gram of protein per pound of your ideal bodyweight. Keep carbohydrates to a handfiul for lunch and dinner. Breakfast should be entirely protein and fats (eg eggs, fish, steak and almonds).
When snacking, snack only on protein.
Ketones/ Atkins/ special K diet/ etc-
Steer well clear from! Short time diets virtually always result in rapid weight loss followed by a large increase in weight gain soon after the diet ends. Statistically around 97% of people that go on diets, end up gaining more weight than they started with!
Calories vs calories out diet
Using your BMR (you can calculate it online) you can work out how many calories your body needs to consume daily. Once you've found the number, simply eat 500kcals less each day (ideally from carbs) Whilst it's impossible to measure your BMR 100% accurately, this method does work.
The only problem with this method is that not all calories are created equal. An apple and a kitkat have approx the same kcals but whilst the chocolate will convert immediately in to fat cells, the apple will digest slowly in your stomach and the vast majority will pass straight though you.
One last thought- DONT DRINK YOUR CALORIES!
All alcoholic drinks contain many calories as do milkshakes and soft drinks. They're simply not worth it