I think you may have it the wrong way around MD6. When you begin to run, you use up sugar in the form of Glucose which is present in your blood. The normal level is 90mg Glucose/100ml of blood. As you begin to run your muscle cells begin to respire more - using up Glucose to produce energy in the form of ATP - they will use up this Glucose.
In the Pancreas, there are little groups of cells called Islets of Langerhan. These respond to changes in blood glucose. In the case of running, your blood glucose will fall too low. So the hormone Glucagon is released. This binds to Liver cells - Hepatocytes - and causes them to turn stored Glucose in the from of Glycogen into Glucose which then enters the blood stream. When this store of Glycogen is used up, then you start to burn fat (Lipids).
Your body doesn't particuarly want to burn fat, it would much prefer Glucose as it is produces energy less efficiently. This can be measured by looking at the RQ value or Respiratory Quotient. This is calculated by:
RQ = CO2 Produced / O2 Used Up
Lipids have a value of about 0.7, carbs (ie glucose) have a value of 1. This means respiring lipids produces more CO2, which is not good as it affects blood pH and other bad things.
Hope this is comprehensive, you guys just helped me revise for my A-level bio exam on thursday

Any more questions, throw em my way and I'll give them a bash.