1. Intense Strength Training -- Without a doubt this is the best exercise for boosting the metabolism, burning fat, losing lbs, and keeping/increasing muscle. It basically involves doing short workouts based around high-intensity sets of compound resistance movements. Intense strength training helps to burn fat extremely efficiently in 3 main ways:
-- Requires lots of energy (calories) during the actual workout
-- Re-building/repairing muscle tissue uses up lots of energy during the 1-2 days after the workout
-- The new lean muscle tissue you're left with (if you're consuming enough protein/calories) will boost your metabolism and allow you to continue burning fat fast
2. Protein-based, Quality Carb Diet -- The best diet for burning fat, losing pounds, and building is one based around protein, healthy fats, and only "quality" carbohydrates. Protein is necessary because it provides the amino acids that build that vital lean muscle mass. Healthy fats are necessary because you're body needs them to function optimally and have a strong metabolism. Carbs are where things get a little tricky. You definitely need some to enjoy good health and high energy levels. But it's very easy to overdo it, especially if you're consuming large amounts of highly-processed carbs (e.g. refined sugars and flours) and/or "white" starches (e.g. white potatoes, white rice, etc.).
The best solution is often to limit your carb intake to mainly vegetables, fruits, and beans/legumes. Add in some healthy natural starches like whole grains, sweet potatoes, etc. in a strategic way that allows your body to use the calories and insulin-boost well (e.g. eating them only after your strength training workouts).
3. Smart Cardio -- Cardio exercise can definitely help you burn fat faster. But, like starchy carbs, it's easy to overdo it and end up burning lots of lean muscle as well. The best option is to do mostly short, variable-intensity cardiovascular workouts such as HIIT-style interval training. This is proven to speed up fat loss while also limiting muscle loss. You should also practice a fun sport or higher-intensity activity like hiking at least once or twice a week.
So there you go: the best way to burn fat, lose pounds, and keep or increase that ultra-important lean muscle tissue. Use the tips above and you'll get that lean, toned, and sexy "fitness model" body you've always wanted!