The marginal cost and average cost curves are both normally drawn u-shaped due to increasing and then diminishing returns. Marginal cost will always intersect the average cost at the minimum point of the average cost curve.
Both these curves are short run curves. The firm will be constrained in the short run by their fixed factors. As these cannot be changed, they can only alter their variable factors. As they do this, they will initially experience increasing returns and so MC and AC will both fall. However, eventually they will experience diminishing returns and MC and AC will start to rise again.