There are a total of 25 VIP levels. To upgrade your VIP level you need to obtain VIP points. You can buy them for gold in the “Upgrade VIP status” window, draw them from clan chests or purchase as part of game offers. The higher your VIP level, the more points you need to upgrade it.
In order to add points to your VIP level, open the main menu and hit the small "+" icon below your VIP level progress (right corner below the next level number). Use relevant items from the menu that pops up next. You can use multiple VIP points items in the VIP points interface by pressing the >> button, which is a unique Premium feature (it will only be available if you have purchased Premium).