Well, it's pretty simple. Pretty much any training that you do that improves your aerobic capacity will increase your fat-burning potential. Interval training is a traditional - and successful - way of doing this.
If you increase your aerobic capacity, you can generate more power from fat and will therefore need to use less carbohydrate for a given power level. However, most cyclists just use this increase to ride faster, so it's a bit of a wash. If you watch pro racers - who have epic ability to burn fat - you'll notice they are sucking down the carbs pretty much all the time.
Two other answers mention bonk training. The research around the effect of riding with low glycogen stores isn't very clear - some studies say it helps, other say no. If you do want to do it, there is no requirement, however, that you go all the way to the bonk.