I'm studying professional nutrition and work in a clinic where the doctors get similar questions. One major tip is to eat more healthy fats and oils to get your body used to burning more fats.
Foods like nuts, avocados, olive oils, and fatty fish. Grapefruit is also highly recommended.
Side Note: The muscles don't burn fat directly. They run on stored glycogen (condensed glucose) and blood glucose. When that runs out they call on the liver to convert it's stores of glycogen to glucose and send it via the bloodstream to to muscles. The liver then works to replenish its glycagen stores with the easiest energy source available (your last meal or two).
If you've been eating lots of healthy fats and oils the liver will adapt to being more efficient at burning those. Thus, when you do a lot of exericise the liver will use more body fats to make glucose for your muscles.
Reference: Principle of Anatomy and Physiology, by Gerard Totora and Bryan Derrickson.