It's natural to think that if you tend to walk on the outsides of your feet that you should add support to the outside of your feet to help "turn" the feet inward. While this will sometimes work, it treats a symptom of supination more than the cause.
The cause of supination is the outwards rolling of the ankle during movement. While outside foot support will help correct for this motion, it doesn't actually prevent the motion directly.
Orthotic support for the foot will help the foot pronate normally by cradling the heel and aligning the foot such that it pronates normally. This is the best treatment and prevention strategy for supination.