Without using cleanses or colinics what is the best way to remove built up waste inside the intestines?

No colonics please. The bacteria in your bowel have a role and are supposed to be there to help with many physiologic functions. Eating plenty of fiber (vegetables, fruits, whole grains etc) is usually sufficient to create bulk and empty your bowels. Published data shows that colonics are dangerous ( and i would add, a real waste of money ).
Misconception. This is a common misconception and used by non-professionals to sell their products. Waste does not build up in your intestines, unless there is an obstruction.