Paid Membership
Sign up for a paid membership with RuneScape. Many of the best items, including the Draconic Visage, are available only to paying players. Paid memberships almost double the size of the game, giving players exclusive abilities, areas, quests, modes of transportation and quite a bit more.
Kill Dragons
Confront a high-level dragon. Black Dragons, Frost Dragons, Iron Dragons, King Black Dragons, Mithril Dragons, Skeletal Wyverns, and Steel Dragons are the only enemies that have a chance of dropping the Draconic Visage upon death. Each of these creatures is extremely difficult to kill, ranging in level from 140 to 304, so make sure before confronting them that you are of an appropriate level and that you are equipped in the proper manner. The Draconic Visage is a very rare drop, so it will take a significant invest of time to acquire it this way.
Trade with Other Players
The Draconic Visage is a tradable item. This means that players who acquire it, but don't want it, can trade it to other players. Because this is a common item for players to want, some players farm the Visage to sell for a profit. Ask around when in towns, and you may be able to find a deal.
The Market Place Forums
The official "RuneScape" forum has a Market Place Forum where players can request items or reply to current threads about items to make offers. The Draconic Visage is a common item to find listed here for sale, and buying it is undoubtedly the quickest way to acquire it. Be prepared to pay a steep price.