'Veininess' or vascularity is something of a genetic cointoss... even at my most muscular and lowest bodyfat percentages I was not particularly veiny. Having said that, diet and exercise are the keys... as your body burns fat from its stores, slowly it will 'move around' your body seeking fat deposits to consume. Other than 'brown fat' around your organs, I think one of the last areas to burn is subcutaneous fat.