To wear a vest, put a good-fitting vest on over a snug-fitting shirt. Then make sure the vest covers the natural waistline, so the shirttail doesn't show.
A good-fitting vest will fit a little bit snugly. For a polished look, the vest fabric should lay flat against the body, with no saggy places. The fabric around the armholes should not stick out, and the vest's neckline should fall into a v-shape below the shirt's collar, right about mid-chest level. If worn with a dress shirt and tie, the tie should be tucked into the v of the vest's neckline. A vest can be worn with or without a jacket, but if worn with a jacket, it is extra useful to have the vest fit snugly to avoid bulkiness.