The Best Way To Lose Fat And Build Muscle

Lose Fat
The first half of the equation is losing fat. This is a simple formula, but one which unfortunately contradicts the ideals of building muscle as we'll see in a minute.
Fat is surplus calories stored on your body for later on. This is an ability we developed thousands of years ago when food was in short supply and we needed to make sure we didn't waste a single calorie.
If you eat more calories than you burn during the day, any spare calories are converted to fat and stored on your body. If you eat LESS calories than you burn during the day, your body will turn to your fat stores to keep itself going, and so you burn off your fat.
More calories = fat.
Less calories = burning off the fat!
There is no magic technique for losing fat. The process is as simple as: eat less calories during the day. OR, if you want to keep your calories high you can do more physical exercise to increase the amount of calories you burn. Either way you'll end up using more than you've eaten and your body will burn off fat instead.
Building Muscle
As I mentioned before, building muscle is the difficult contradiction to the above. In order to build muscle, you need MORE calories than usual because it takes a lot of energy to grow new muscle.
This makes losing fat and building muscle at the same time difficult, but not impossible. The idea is to keep your calories fairly even instead of raising or lowering them. Then as you progress through your training regime you can monitor your results and adjust your calories accordingly.
Admittedly, this approach means you may not necessarily be able to lose fat as fast as you could, or gain muscle as fast as you could, but you'll look better, faster, as you zone in on your ideal physique.
Keep your fat and sugar intake low, your protein intake high, and your carbohydrate intake moderate. Weight yourself and measure your key stats (chest, biceps, thighs, waist) regularly to watch for changes. 
Above all else, make sure you're following a proper and well thought out training and diet plan. There's nothing worse than getting it wrong for 3-6 months and realising you've made no progress. Get some professional help and make sure you get it right from the beginning.