First thing's first: do NOT ask the local shops advice, they will try and sell you every product on the shelf.
Calories out > Calories in
That is how you lose body fat. In other words, it's all in the diet.
As for where to start? Well, as far as the gym is concerned you want to learn all of the major compound movements. This includes the bench press, dead lift, squat and press (called the military press most of the time). I recommend Starting Strength by Mark Rippetoe. He has a science degree and takes a very analytically approach to the movements. I wouldn't recommend going without it, but he also has a video detailing the same stuff if you'd care to see it visually; I'd say get both if you can afford it, as it will cover about 95% of any instruction you'll ever need in the weight room.
Since your goal is to burn fat, you need to cut your carbs, and up your protein.
Make sure you get 1-2 servings of essential fatty acids every day (commonly abbreviated EFA). Examples include nuts (almonds, peanuts, yes even peanut butter but only the natural stuff you find at whole foods), fish, fish oil, avocado, flax, etc.
Eat a minimum of 3 servings of fruit and vegetables (so 6 servings total) every day. Other sources of carbs that are good would be:
oats, whole grain breads, pastas, etc, yams (called sweet potatoes in the United States, the orange stuff, looks like a tree root in full form), etc.
Refer to the sticky post "how to cut" in the fat loss forum for additional examples. You just need to eat clean, and eat less than you need to maintain your body. In that sense it's that simple, but if you have never been taught how to eat healthy then you have a lot of research to do.