Insulin stimulates the activity of pyruvate dehydrogenase phosphatase.  The phosphatase removes the phosphate from pyruvate dehydrogenase activating it and allowing for conversion of pyruvate to acetyl-CoA.  This mechanism leads to the increased rate of catalysis of this enzyme, so increases the levels of acetyl-CoA. Increased levels of acetyl-CoA will increase the flux through not only the fat synthesis pathway but also the citric acid cycle.