Visit the Apple App Store, and select the premium Dictionary Pro application. If you have previously purchased this app, make sure to use the same Apple ID you used to make your initial purchase.
Please note that you cannot upgrade to the Premium version of the app from the Free version. They are in fact two separate apps, and in order to use the Dictionary.com Pro, you will need to download it separately from the App Store. The easiest way to tell the difference is to look for the silver lining around the app icon.