The ability to customize your iOS device beyond a wallpaper on the home and lock screens and icon arrangement doesn't truly exist. Unless, that is, you decide to jailbreak your iDevice. Jailbreaking a device gives you full permission to modify and install whatever you want on iOS, outside of Apple's walled garden. There are plenty of arguments for and against the act, but we'll leave that for another post.
For those who don't want to jailbreak, a new app called Iconical will allow you to create your own app icon for a long list of supported apps (the developer claims 14,000 apps are supported).
You can purchase Iconical from the App Store for $1.99, or if you're fast enough you can get it for half price for the next week.
After you install it, you can select an app from the default list, or scan the installed apps on your device. How the app works is actually pretty ingenious. Iconical will scan for installed apps that support the iOS URL scheme, which allows apps to be launched from another location, either to the default or with a specific function in mind. An example of a specific function includes launching the FaceTime app and calling a predefined contact just by tapping on the icon. The icon you end up creating is nothing more than a Web shortcut pointing to a URL scheme.
Select an app and begin designing. You're able to draw, import a photo, or take a new photo to replace the current icon.
Once you've added a photo and given your icon a name, simply tap on the "Create Home Screen Icon" text. You'll then be redirected to Safari on your device, where you're instructed to create a Web shortcut.
In the end, you'll have the default app icon on your device, along with the newly created icon. You can hide the standard icon(s) in a folder and move your creation into its place on your home screen.