It's not a dumb question, its actually very good. I asked the same thing when I started my healthy lifestyle.
When you are not eating, your body is not absorbing food. If your body is not absorbing food, there are lower levels of insulin in the blood. However, your body is always using energy, so if you're not absorbing food, this energy must come from internal stores of complex carbohydrates, fats and proteins.
Your bodies' main source of energy is glucose, which it uses as fuel first, before going on to break down the fat cells into fatty acids. It is these fatty acids which need to be broken down for energy, that determine your fat loss.
Your weight is determined by the rate at which you store energy from the food that you eat, and the rate at which you use that energy. Remember that as your body breaks down fat, the number of fat cells remains the same; each fat cell simply gets smaller.
The way I lost my weight, although I hate using that term (I prefer "got healthy"), was to eat a healthy, balanced diet of around 1500 calories a day and combine it with a regular exercise routine. There is a review of the system Here.
The exercise routine is the key factor. Your diet will only go so far to burning fat, whereas exercise will quickly use glucose reserves before breaking down the fat cells into fatty acids and releasing them into your bloodstream.
The system I used has a strong emphasis on 10-20 minutes HIIT (High Intensity Interval Training) which accomplishes the above, which is then followed by 15 minutes or so off relaxing exercise (a jog/brisk walk or cycling).
So, my workout would generally be 30 seconds on the bike as fast as I can, followed immediately by 30 seconds slowly cyling and recovering - then repeat process 15 times. After that 15 minutes of normal cardio actually burns the fatty acids in the bloodstream, using them for "fuel". This in my opinion, is the fastest way to drop fat in your body.
This exercise routine (with a weights routine alongside it to shape/,ould the muscles to how you want) combined with your fuel (healthy, balanced diet) literally melts fat way.
I hope that helps, I tried to make it as non-technical as possible.