Showing one's best is essentially different from showing off. It is a quality not everybody can be good at.
In order to show your best, you are advised to do three things. First, you should equip yourself with the knowledge you can acquire. Only thus can you be confident of yourself. Second in importance is a good command of verbal skills. This is how effectively you will be able to make yourself convincing. My last advice is modesty. Don't let others suspect you are being arrogant and showing off.