There's no "right" way for everyone to lose fat, but one thing's for sure, spot-reduction does not happen, period. Most people will have a "stubborn" area that's the last to go (for me, it's the lower belly and love handles, always hanging around until the last minue...)
Some do well on high protein (like myself), some do better on lower fat/high carbohydrates, but one thing's for sure, you'll want to keep track of everything you eat, learn your baseline caloric intake for maintaining your current weight, and cut a bit off the top of that as well as do weight training and cardio for the best effects. You can't lose fat if you take in more calories than your body can burn in a day, so learning where your maintenance caloric intake levels are is the best place to begin. Make sure you spend about a week eating around what you THINK your baseline is for keeping weight stable (if you think it's around, say, 1800 calories/day, start there, shoot for that amount of calories each day for a week or two, and track your weight and get bodyfat measurements before and after. If anything goes up more than a fraction (to account for water weight fluctuations), you may find that you need to lower your intake accordingly, perhaps by cutting 200-300 cal./day and doing a bit of light cardio. If you lose weight at that level, then you know you can eat more to maintain, and then you're at a good point to begin tracking how much you should be eating for your first stretch into a fat loss program.
One thing's for sure, fasts/cleanses don't flush out fat - you may "detox", but you're likely going to lose as much muscle or more than any fat lost, and that can actually INCREASE your overall bodyfat percentage while decreasing your weight. Your body, when in starvation mode, will eat away at muscle for fuel first as a preferred source, which is the LAST thing anyone wants when trying to lose fat. Muscle loss will reduce how many calories your body burns during the day, not to mention it will add to the visual effect of having more fat even if your bodyfat levels stay the same while losing muscle. Definitely not a good way to try and lose fat under any circumstances, because even worse, if you overeat at all after coming off of a fast, you'll rebound and likely put on fat at a much faster rate than ever. If you want to "detox", then a short fast is fine, but if you want to lose fat, it's going to be a major roadblock to progress and may well do more harm than good in the end.
Slow and sensible is always the best way, the more radical the plan, the more likely the effects will turn against you if things are not done 100% perfectly. There's no magic bullet for fat loss that works on everyone, it's a matter of experimenting with various methods of diet and training until you finally find what your own body responds to best (nothing works well for everyone, no matter how much there may be people claiming it does, some programs simply are bad for some individuals).
Best of success in your journey!
"A 'hardgainer' is merely someone who hasn't bothered to try enough different training methods to learn what is actually right for their own damned body." - anonymous